J. Gonera - Academia.edu (original) (raw)
Papers by J. Gonera
Physical Review D, 2002
The nullification of threshold amplitudes is considered within the conventional framework of quan... more The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.
A geometric picture of conformally invariant mechanics is presented. Although the standard form o... more A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.
It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symm... more It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.
The orbit method is used to describe the centre of mass motion of the system of particles with fi... more The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.
The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrument... more The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case. Star escape from a Galaxy is studied as application.
We consider the dynamics invariant under the action of l-conformal Galilei group using the method... more We consider the dynamics invariant under the action of l-conformal Galilei group using the method of nonlinear realizations. We find that by an appropriate choice of the coset space parametrization one can achieve the complete decoupling of the equations of motion. The Lagrangian and Hamiltonian are constructed. The results are compared with those obtained by Galajinsky and Masterov [Nucl. Phys. B860, (2013), 212].
The higher-derivative theories with degenerate frequencies exhibit BRST symmetry (O. Rivelles, Ph... more The higher-derivative theories with degenerate frequencies exhibit BRST symmetry (O. Rivelles, Phys. Lett. B577 (2003), 147). In the present paper meaning of BRST invariance condition is analyzed. The BRST symmetry is related to nondiagonalizability of the Hamiltonian and it is shown that BRST condition singles out the subspace spanned by proper eigenvectors of the Hamiltonian.
The quasiclassical theory of massless chiral fermions is considered. The effective action is deri... more The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
Nuclear Physics B, 2014
It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conform... more It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ω k = (2k − 1)ω 1 , where k = 1,. .. , n, and l is the half-integer 2n−1 2. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton-Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.
All unitary irreducible representation of centrally extended (Nodd) N-conformal Galilei group are... more All unitary irreducible representation of centrally extended (Nodd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in: J. Gomis, K. Kamimura, Phys. Rev. D85 (2012), 045023.
The conformal transformations corresponding to N-Galilean conformal symmetries, previously define... more The conformal transformations corresponding to N-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.
The orbit method is used to describe the centre of mass motion of the system of particles with fi... more The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart-Duval lift.
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As c... more The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.
arXiv: High Energy Physics - Theory, 2007
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It i... more An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian is nonsingular and the Legendre transformation is performed in a straightforward way.
arXiv: High Energy Physics - Theory, 2012
It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symm... more It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.
arXiv: High Energy Physics - Theory, 2011
A geometric picture of conformally invariant mechanics is presented. Although the standard form o... more A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.
It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of... more It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the free Lagrangian involving (N+1)/2-th order time derivative.
The quasiclassical theory of massless chiral fermions is considered. The effective action is deri... more The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As c... more The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.
Journal of Mathematical Physics, 2010
We comment on the recent paper of Di Criscienzo and Zerbini [J. Math. Phys. 50, 103517 (2009)]. W... more We comment on the recent paper of Di Criscienzo and Zerbini [J. Math. Phys. 50, 103517 (2009)]. We argue that the Euclidean evolution operator computed in our paper (K. Andrzejewski et al., e-print arXiv:0904.3055) is correct contrary to the claim of Di Criscienzo and Zerbini.
Physical Review D, 2002
The nullification of threshold amplitudes is considered within the conventional framework of quan... more The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.
A geometric picture of conformally invariant mechanics is presented. Although the standard form o... more A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.
It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symm... more It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.
The orbit method is used to describe the centre of mass motion of the system of particles with fi... more The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.
The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrument... more The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case. Star escape from a Galaxy is studied as application.
We consider the dynamics invariant under the action of l-conformal Galilei group using the method... more We consider the dynamics invariant under the action of l-conformal Galilei group using the method of nonlinear realizations. We find that by an appropriate choice of the coset space parametrization one can achieve the complete decoupling of the equations of motion. The Lagrangian and Hamiltonian are constructed. The results are compared with those obtained by Galajinsky and Masterov [Nucl. Phys. B860, (2013), 212].
The higher-derivative theories with degenerate frequencies exhibit BRST symmetry (O. Rivelles, Ph... more The higher-derivative theories with degenerate frequencies exhibit BRST symmetry (O. Rivelles, Phys. Lett. B577 (2003), 147). In the present paper meaning of BRST invariance condition is analyzed. The BRST symmetry is related to nondiagonalizability of the Hamiltonian and it is shown that BRST condition singles out the subspace spanned by proper eigenvectors of the Hamiltonian.
The quasiclassical theory of massless chiral fermions is considered. The effective action is deri... more The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
Nuclear Physics B, 2014
It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conform... more It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ω k = (2k − 1)ω 1 , where k = 1,. .. , n, and l is the half-integer 2n−1 2. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton-Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.
All unitary irreducible representation of centrally extended (Nodd) N-conformal Galilei group are... more All unitary irreducible representation of centrally extended (Nodd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in: J. Gomis, K. Kamimura, Phys. Rev. D85 (2012), 045023.
The conformal transformations corresponding to N-Galilean conformal symmetries, previously define... more The conformal transformations corresponding to N-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.
The orbit method is used to describe the centre of mass motion of the system of particles with fi... more The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart-Duval lift.
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As c... more The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.
arXiv: High Energy Physics - Theory, 2007
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It i... more An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian is nonsingular and the Legendre transformation is performed in a straightforward way.
arXiv: High Energy Physics - Theory, 2012
It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symm... more It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.
arXiv: High Energy Physics - Theory, 2011
A geometric picture of conformally invariant mechanics is presented. Although the standard form o... more A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.
It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of... more It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the free Lagrangian involving (N+1)/2-th order time derivative.
The quasiclassical theory of massless chiral fermions is considered. The effective action is deri... more The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As c... more The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.
Journal of Mathematical Physics, 2010
We comment on the recent paper of Di Criscienzo and Zerbini [J. Math. Phys. 50, 103517 (2009)]. W... more We comment on the recent paper of Di Criscienzo and Zerbini [J. Math. Phys. 50, 103517 (2009)]. We argue that the Euclidean evolution operator computed in our paper (K. Andrzejewski et al., e-print arXiv:0904.3055) is correct contrary to the claim of Di Criscienzo and Zerbini.