Mauricio Valenzuela - Academia.edu (original) (raw)

Papers by Mauricio Valenzuela

It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can ... more It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can be embedded into a representation of the higher-spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrodinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of non-relativistic generators. We show also how to convert the Vasiliev equations into an explicit non-relativistic covariant form, such that they may apply to non-relativistic systems. Our procedure reveals that the space of solutions of the Schrodinger equation can be regarded also as a supersymmetric module.

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.

Annals of Physics, 2010

Universal vector wave equations allowing for a unified description of anyons, and also of usual b... more Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2 + 1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Lévy-Leblond 's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inönü-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.

Nuclear Physics B, 2007

A covariant set of linear differential field equations, describing an N = 1 supersymmetric anyon ... more A covariant set of linear differential field equations, describing an N = 1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic "Jackiw-Nair" limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N = 1 supersymmetry. *

Physical Review D, 2008

We propose a (3+1)D linear set of covariant vector equations, which unify the spin-0 “new Dirac e... 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 degrees 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 higher-spin 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.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincare symmetry.

Journal of High Energy Physics, 2009

The representation theory underlying the infinite-component relativistic wave equation written by... more The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N = 1 supermultiplet, which carries a super-Poincaré

Nuclear Physics B, 2007

A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon sy... more A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic "Jackiw-Nair" limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N=1 supersymmetry.

Annals of Physics, 2010

Universal vector wave equations allowing for a unified description of anyons, and also of usual b... more Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2+1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Lévy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inönü-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincaré symmetry emerges from the osp(1|2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblondtype" equations which, together, carry an N = 2 superSchrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincaré algebra.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincaré symmetry.

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincar\'e symmetry emerges from the osp(1∣2)osp(1|2)osp(1∣2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "L\'evy-Leblond-type" equations which, together, carry an N=2 superSchr\"odinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincar\'e algebra.

Journal of Mathematical Physics, 2010

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The super-Poincaré symmetry emerges from the osp(1∣2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The nonrelativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblond-type" equations which, together, carry an N =2 super-Schrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the super-Poincaré 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 higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

 Materias Primas al alcance local (metales, plásticos y fibras de carbono se producen ampliament... more  Materias Primas al alcance local (metales, plásticos y fibras de carbono se producen ampliamente en Italia, por lo que el costo de adquisición y traslado es barato)

It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can ... more It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can be embedded into a representation of the higher-spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrodinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of non-relativistic generators. We show also how to convert the Vasiliev equations into an explicit non-relativistic covariant form, such that they may apply to non-relativistic systems. Our procedure reveals that the space of solutions of the Schrodinger equation can be regarded also as a supersymmetric module.

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.

Annals of Physics, 2010

Universal vector wave equations allowing for a unified description of anyons, and also of usual b... more Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2 + 1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Lévy-Leblond 's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inönü-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.

Nuclear Physics B, 2007

A covariant set of linear differential field equations, describing an N = 1 supersymmetric anyon ... more A covariant set of linear differential field equations, describing an N = 1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic "Jackiw-Nair" limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N = 1 supersymmetry. *

Physical Review D, 2008

We propose a (3+1)D linear set of covariant vector equations, which unify the spin-0 “new Dirac e... 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 degrees 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 higher-spin 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.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincare symmetry.

Journal of High Energy Physics, 2009

The representation theory underlying the infinite-component relativistic wave equation written by... more The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N = 1 supermultiplet, which carries a super-Poincaré

Nuclear Physics B, 2007

A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon sy... more A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic "Jackiw-Nair" limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N=1 supersymmetry.

Annals of Physics, 2010

Universal vector wave equations allowing for a unified description of anyons, and also of usual b... more Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2+1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Lévy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inönü-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincaré symmetry emerges from the osp(1|2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblondtype" equations which, together, carry an N = 2 superSchrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincaré algebra.

Physical Review D, 2010

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discr... more The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincaré symmetry.

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincar\'e symmetry emerges from the osp(1∣2)osp(1|2)osp(1∣2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "L\'evy-Leblond-type" equations which, together, carry an N=2 superSchr\"odinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincar\'e algebra.

Journal of Mathematical Physics, 2010

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultip... more The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The super-Poincaré symmetry emerges from the osp(1∣2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The nonrelativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblond-type" equations which, together, carry an N =2 super-Schrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the super-Poincaré 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 higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

 Materias Primas al alcance local (metales, plásticos y fibras de carbono se producen ampliament... more  Materias Primas al alcance local (metales, plásticos y fibras de carbono se producen ampliamente en Italia, por lo que el costo de adquisición y traslado es barato)