Mikhail Plyushchay - Academia.edu (original) (raw)
Papers by Mikhail Plyushchay
After a short discussion of the intimate relation between the generalized statistics and supersym... more After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal algebraic construction associated with the holomorphic nonlinear supersymmetry.
Journal of Physics A: Mathematical and General, 2003
We investigate a U (1) gauge invariant quantum mechanical system on a 2D noncommutative space wit... more We investigate a U (1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2, R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.
Annals of Physics, 2009
We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Pös... more We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Pöschl-Teller system by the Aharonov-Bohm effect for a nonrelativistic particle on the AdS 2. A key role in the supersymmetric structure appearing after reduction by a compact generator of the AdS 2 isometry is shown to be played by the discrete symmetries related to the space and time reflections in the ambient Minkowski space. We also observe that a correspondence between the two quantum non-relativistic systems is somewhat of the AdS/CFT holography nature.
We review the construction of minimally bosonized supersymmetric quantum mechanics and its relati... more We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems.
Nuclear Physics B, 1998
We investigate hidden symmetries of P ,T-invariant system of topologically massive U(1) gauge eld... more We investigate hidden symmetries of P ,T-invariant system of topologically massive U(1) gauge elds. For this purpose, we propose a pseudoclassical model giving rise to this eld system at the quantum level. The model contains a parameter, which displays a quantization property at the classical and the quantum levels and demonstrates a nontrivial relationship between continuous and discrete symmetries. Analyzing the integrals of motion of the pseudoclassical model, we identify U(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. Representing the hidden symmetries in a covariant form, we show that one-particle states realize an irreducible representation of a non-standard super-extension of the (2 + 1)-dimensional Poincar e group labelled by the zero eigenvalue of the superspin.
Nuclear Physics B - Proceedings Supplements, 2001
We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole fie... more We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole field to apply it for finding the alternative treatment of the charge-monopole as a particle with spin, for tracing out the relation of the charge-monopole to the free relativistic anyon and for clarifying the nature of the non-standard nonlinear supersymmetry of the fermion-monopole system.
Lecture Notes in Physics
The class of relativistic spin particle models reveals the 'quantization' of parameters already a... more The class of relativistic spin particle models reveals the 'quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same requirement applied to a non-relativistic particle with odd degrees of freedom gives rise to supersymmetric quantum mechanics. Coupling classical non-relativistic superparticle to a 'U(1) gauge field', one can arrive at the quantum dynamical supersymmetry. This consists in supersymmetry appearing at special values of the coupling constant characterizing interaction of a system of boson and fermion but disappearing in a free case. Possible relevance of this phenomenon to high-temperature superconductivity is speculated. * Based on invited talk given at the International Seminar "Supersymmetries and Quantum Symmetries" dedicated to the
Nuclear Physics B, 2001
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quan... more The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to a supersymmetric canonical system with the holomorphic form of the supercharges. Depending on the behaviour of the superpotential, the canonical supersymmetric systems are separated into the three classes. In one of them the parameter specifying the supersymmetry order is subject to some sort of classical quantization, whereas the supersymmetry of another extreme class has a rather fictive nature since its fermion degrees of freedom are decoupled completely by a canonical transformation. The nonlinear supersymmetry with polynomial in momentum supercharges is analysed, and the most general one-parametric Calogero-like solution with the second order supercharges is found. Quantization of the systems of the canonical form reveals the two anomalyfree classes, one of which gives rise naturally to the quasi-exactly solvable systems. The quantum anomaly problem for the Calogero-like models is "cured" by the specific superpotential-dependent term of order 2. The nonlinear supersymmetry admits the generalization to the case of two-dimensional systems.
Journal of High Energy Physics, 1998
A pseudoclassical model for P ,T-invariant system of topologically massive U(1) gauge fields is a... more A pseudoclassical model for P ,T-invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of "classical quantization". It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P ,T-invariant quantum system realizes an irreducible representation of a non-standard super-extension of the (2 + 1)-dimensional Poincaré group.
Physical Review D, 2014
We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r 2 pot... more We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r 2 potential reveals a hidden, partially free dynamics when the strength of the central potential and the charge-monopole coupling constant are mutually fitted to each other. In this case the system admits both a conserved Laplace-Runge-Lenz vector and a dynamical conformal symmetry. The supersymmetrically extended system corresponds then to a background of a self-dual or anti-self-dual dyon. It is described by a quadratically extended Lie superalgebra D(2, 1; α) with α = 1/2, in which the bosonic set of generators is enlarged by a generalized Laplace-Runge-Lenz vector and its dynamical integral counterpart related to Galilei symmetry, as well as by the chiral Z 2-grading operator. The odd part of the nonlinear superalgebra comprises a complete set of 24 = 2 × 3 × 4 fermionic generators. Here a usual duplication comes from the Z 2-grading structure, the second factor can be associated with a triad of scalar integrals-the Hamiltonian, the generator of special conformal transformations and the squared total angular momentum vector, while the quadruplication is generated by a chiral spin vector integral which exits due to the (anti)-self-dual nature of the electromagnetic background.
Journal of High Energy Physics, 2009
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic ... more A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic field. Due to supersymmetry, the boundary critical phase which separates the suband super-critical cases can be viewed as reduction to the zero-energy eigensubspace. In the sub-critical phase the system is described by the superextension of exotic Newton-Hooke symmetry, combined with the conformal so(2, 1) ∼ su(1, 1) symmetry; the latter is changed into so(3) ∼ su(2) in the super-critical phase. In the critical phase the spin degrees of freedom are frozen and the supersymmetry disappears.
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of t... more (2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.
Journal of High Energy Physics, 2003
It is shown that the quantization of a superparticle propagating in an N = 1, D = 4 superspace ex... more It is shown that the quantization of a superparticle propagating in an N = 1, D = 4 superspace extended with tensorial coordinates results in an infinite tower of massless spin states satisfying the Vasiliev unfolded equations for free higher spin fields in flat and AdS 4 N = 1 superspace. The tensorial extension of the AdS 4 superspace is proved to be a supergroup manifold OSp (1|4). The model is manifestly invariant under OSp (N |8) (N=1,2) superconformal symmetry. As a byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n) groups are GL (2n) flat, i.e. they are equivalent to flat Cartan forms up to an exactly determined GL (2n) rotation. This property is crucial for carrying out the quantization of the particle model on OSp (1|4) and getting the higher spin field dynamics in super AdS 4 , which can be performed in a way analogous to the flat case.
Journal of High Energy Physics, 2003
We show that a simple change of the classical boson-fermion coupling constant, 2α → 2αn, n ∈ N, i... more We show that a simple change of the classical boson-fermion coupling constant, 2α → 2αn, n ∈ N, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1, 2) × u(1) subalgebra, and by the 2(n + 1) fermionic integrals constituting the two spin-n 2 so(1, 2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter α is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with |α| = p, p ∈ N, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.
Physics Letters B, 1993
A new pseudoelassical model is proposed for the description of the relativistic massive Dirac par... more A new pseudoelassical model is proposed for the description of the relativistic massive Dirac particle. It is Pand T-noninvariant in the case of odd space-time dimensions. The quantization of the model leads exactly to the corresponding d-dimensional Dirac equation for arbitrary d, conserving its P-and T-noninvariance at the quantum level for the case of odd d.
Physics Letters B, 2000
It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De ... more It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De Jonghe, Macfarlane, Peeters and van Holten, and the generator of its standard N = 1/2 supersymmetry have to be supplemented by their product operator to be treated as independent supercharge. As a result, the fermion-monopole system possesses the nonlinear N = 3/2 supersymmetry having the nature of the 3D spin-1/2 free particle's supersymmetry generated by the supercharges represented in a scalar form. Analyzing the supercharges' structure, we trace how under reduction of the fermion-monopole system to the spherical geometry the nonlinear N = 3/2 superalgebra comprising the Hamiltonian and the total angular momentum as even generators is transformed into the standard linear N = 1 superalgebra with the Hamiltonian to be the unique even generator.
Physics Letters B, 2003
We show that the reduction of a planar free spin-1 2 particle system by the constraint fixing its... more We show that the reduction of a planar free spin-1 2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight n ∈ N, n > 1, and subsequent application of the Dirac reduction procedure ('first quantize and then reduce') give rise to the anomaly free quantum system with the order n nonlinear superconformal symmetry constructed recently in hep-th/0304257. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form.
Physics Letters B, 1997
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclass... more A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge) and discrete symmetries of the corresponding systems, but there are some special discrete values of them which give rise to the maximal global symmetries at the classical level. Exactly the same values of the parameters are separated at the quantum level, where, in particular, they are singled out by the requirement of conservation of the discrete symmetries. The phenomenon is observed for the familiar pseudoclassical model of 3D P, T-invariant massive fermion system and for a new pseudoclassical model of 3D P, T-invariant system of topologically massive U(1) gauge fields.
Physics Letters B, 2004
We study a longstanding problem of identification of the fermion-monopole symmetries. We show tha... more We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z 2-graded Poisson, or quantum super-algebra, which may be treated as a nonlinear generalization of the osp(2|2)⊕ su(2). In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.
Physical Review D, 2008
We propose a (3 + 1)D linear set of covariant vector equations, which unify the spin 0 "new Dirac... more We propose a (3 + 1)D linear set of covariant vector equations, which unify the spin 0 "new Dirac equation" with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0, 1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higherspin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincaré algebra with or without tensorial central charge.
After a short discussion of the intimate relation between the generalized statistics and supersym... more After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal algebraic construction associated with the holomorphic nonlinear supersymmetry.
Journal of Physics A: Mathematical and General, 2003
We investigate a U (1) gauge invariant quantum mechanical system on a 2D noncommutative space wit... more We investigate a U (1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2, R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.
Annals of Physics, 2009
We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Pös... more We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Pöschl-Teller system by the Aharonov-Bohm effect for a nonrelativistic particle on the AdS 2. A key role in the supersymmetric structure appearing after reduction by a compact generator of the AdS 2 isometry is shown to be played by the discrete symmetries related to the space and time reflections in the ambient Minkowski space. We also observe that a correspondence between the two quantum non-relativistic systems is somewhat of the AdS/CFT holography nature.
We review the construction of minimally bosonized supersymmetric quantum mechanics and its relati... more We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems.
Nuclear Physics B, 1998
We investigate hidden symmetries of P ,T-invariant system of topologically massive U(1) gauge eld... more We investigate hidden symmetries of P ,T-invariant system of topologically massive U(1) gauge elds. For this purpose, we propose a pseudoclassical model giving rise to this eld system at the quantum level. The model contains a parameter, which displays a quantization property at the classical and the quantum levels and demonstrates a nontrivial relationship between continuous and discrete symmetries. Analyzing the integrals of motion of the pseudoclassical model, we identify U(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. Representing the hidden symmetries in a covariant form, we show that one-particle states realize an irreducible representation of a non-standard super-extension of the (2 + 1)-dimensional Poincar e group labelled by the zero eigenvalue of the superspin.
Nuclear Physics B - Proceedings Supplements, 2001
We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole fie... more We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole field to apply it for finding the alternative treatment of the charge-monopole as a particle with spin, for tracing out the relation of the charge-monopole to the free relativistic anyon and for clarifying the nature of the non-standard nonlinear supersymmetry of the fermion-monopole system.
Lecture Notes in Physics
The class of relativistic spin particle models reveals the 'quantization' of parameters already a... more The class of relativistic spin particle models reveals the 'quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same requirement applied to a non-relativistic particle with odd degrees of freedom gives rise to supersymmetric quantum mechanics. Coupling classical non-relativistic superparticle to a 'U(1) gauge field', one can arrive at the quantum dynamical supersymmetry. This consists in supersymmetry appearing at special values of the coupling constant characterizing interaction of a system of boson and fermion but disappearing in a free case. Possible relevance of this phenomenon to high-temperature superconductivity is speculated. * Based on invited talk given at the International Seminar "Supersymmetries and Quantum Symmetries" dedicated to the
Nuclear Physics B, 2001
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quan... more The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to a supersymmetric canonical system with the holomorphic form of the supercharges. Depending on the behaviour of the superpotential, the canonical supersymmetric systems are separated into the three classes. In one of them the parameter specifying the supersymmetry order is subject to some sort of classical quantization, whereas the supersymmetry of another extreme class has a rather fictive nature since its fermion degrees of freedom are decoupled completely by a canonical transformation. The nonlinear supersymmetry with polynomial in momentum supercharges is analysed, and the most general one-parametric Calogero-like solution with the second order supercharges is found. Quantization of the systems of the canonical form reveals the two anomalyfree classes, one of which gives rise naturally to the quasi-exactly solvable systems. The quantum anomaly problem for the Calogero-like models is "cured" by the specific superpotential-dependent term of order 2. The nonlinear supersymmetry admits the generalization to the case of two-dimensional systems.
Journal of High Energy Physics, 1998
A pseudoclassical model for P ,T-invariant system of topologically massive U(1) gauge fields is a... more A pseudoclassical model for P ,T-invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of "classical quantization". It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P ,T-invariant quantum system realizes an irreducible representation of a non-standard super-extension of the (2 + 1)-dimensional Poincaré group.
Physical Review D, 2014
We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r 2 pot... more We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r 2 potential reveals a hidden, partially free dynamics when the strength of the central potential and the charge-monopole coupling constant are mutually fitted to each other. In this case the system admits both a conserved Laplace-Runge-Lenz vector and a dynamical conformal symmetry. The supersymmetrically extended system corresponds then to a background of a self-dual or anti-self-dual dyon. It is described by a quadratically extended Lie superalgebra D(2, 1; α) with α = 1/2, in which the bosonic set of generators is enlarged by a generalized Laplace-Runge-Lenz vector and its dynamical integral counterpart related to Galilei symmetry, as well as by the chiral Z 2-grading operator. The odd part of the nonlinear superalgebra comprises a complete set of 24 = 2 × 3 × 4 fermionic generators. Here a usual duplication comes from the Z 2-grading structure, the second factor can be associated with a triad of scalar integrals-the Hamiltonian, the generator of special conformal transformations and the squared total angular momentum vector, while the quadruplication is generated by a chiral spin vector integral which exits due to the (anti)-self-dual nature of the electromagnetic background.
Journal of High Energy Physics, 2009
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic ... more A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic field. Due to supersymmetry, the boundary critical phase which separates the suband super-critical cases can be viewed as reduction to the zero-energy eigensubspace. In the sub-critical phase the system is described by the superextension of exotic Newton-Hooke symmetry, combined with the conformal so(2, 1) ∼ su(1, 1) symmetry; the latter is changed into so(3) ∼ su(2) in the super-critical phase. In the critical phase the spin degrees of freedom are frozen and the supersymmetry disappears.
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of t... more (2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.
Journal of High Energy Physics, 2003
It is shown that the quantization of a superparticle propagating in an N = 1, D = 4 superspace ex... more It is shown that the quantization of a superparticle propagating in an N = 1, D = 4 superspace extended with tensorial coordinates results in an infinite tower of massless spin states satisfying the Vasiliev unfolded equations for free higher spin fields in flat and AdS 4 N = 1 superspace. The tensorial extension of the AdS 4 superspace is proved to be a supergroup manifold OSp (1|4). The model is manifestly invariant under OSp (N |8) (N=1,2) superconformal symmetry. As a byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n) groups are GL (2n) flat, i.e. they are equivalent to flat Cartan forms up to an exactly determined GL (2n) rotation. This property is crucial for carrying out the quantization of the particle model on OSp (1|4) and getting the higher spin field dynamics in super AdS 4 , which can be performed in a way analogous to the flat case.
Journal of High Energy Physics, 2003
We show that a simple change of the classical boson-fermion coupling constant, 2α → 2αn, n ∈ N, i... more We show that a simple change of the classical boson-fermion coupling constant, 2α → 2αn, n ∈ N, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1, 2) × u(1) subalgebra, and by the 2(n + 1) fermionic integrals constituting the two spin-n 2 so(1, 2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter α is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with |α| = p, p ∈ N, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.
Physics Letters B, 1993
A new pseudoelassical model is proposed for the description of the relativistic massive Dirac par... more A new pseudoelassical model is proposed for the description of the relativistic massive Dirac particle. It is Pand T-noninvariant in the case of odd space-time dimensions. The quantization of the model leads exactly to the corresponding d-dimensional Dirac equation for arbitrary d, conserving its P-and T-noninvariance at the quantum level for the case of odd d.
Physics Letters B, 2000
It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De ... more It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De Jonghe, Macfarlane, Peeters and van Holten, and the generator of its standard N = 1/2 supersymmetry have to be supplemented by their product operator to be treated as independent supercharge. As a result, the fermion-monopole system possesses the nonlinear N = 3/2 supersymmetry having the nature of the 3D spin-1/2 free particle's supersymmetry generated by the supercharges represented in a scalar form. Analyzing the supercharges' structure, we trace how under reduction of the fermion-monopole system to the spherical geometry the nonlinear N = 3/2 superalgebra comprising the Hamiltonian and the total angular momentum as even generators is transformed into the standard linear N = 1 superalgebra with the Hamiltonian to be the unique even generator.
Physics Letters B, 2003
We show that the reduction of a planar free spin-1 2 particle system by the constraint fixing its... more We show that the reduction of a planar free spin-1 2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight n ∈ N, n > 1, and subsequent application of the Dirac reduction procedure ('first quantize and then reduce') give rise to the anomaly free quantum system with the order n nonlinear superconformal symmetry constructed recently in hep-th/0304257. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form.
Physics Letters B, 1997
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclass... more A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge) and discrete symmetries of the corresponding systems, but there are some special discrete values of them which give rise to the maximal global symmetries at the classical level. Exactly the same values of the parameters are separated at the quantum level, where, in particular, they are singled out by the requirement of conservation of the discrete symmetries. The phenomenon is observed for the familiar pseudoclassical model of 3D P, T-invariant massive fermion system and for a new pseudoclassical model of 3D P, T-invariant system of topologically massive U(1) gauge fields.
Physics Letters B, 2004
We study a longstanding problem of identification of the fermion-monopole symmetries. We show tha... more We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z 2-graded Poisson, or quantum super-algebra, which may be treated as a nonlinear generalization of the osp(2|2)⊕ su(2). In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.
Physical Review D, 2008
We propose a (3 + 1)D linear set of covariant vector equations, which unify the spin 0 "new Dirac... more We propose a (3 + 1)D linear set of covariant vector equations, which unify the spin 0 "new Dirac equation" with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0, 1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higherspin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincaré algebra with or without tensorial central charge.