86 research outputs found
BRST analysis of general mechanical systems
We study the groups of local BRST cohomology associated to the general
systems of ordinary differential equations, not necessarily Lagrangian or
Hamiltonian. Starting with the involutive normal form of the equations, we
explicitly compute certain cohomology groups having clear physical meaning.
These include the groups of global symmetries, conservation laws and Lagrange
structures. It is shown that the space of integrable Lagrange structures is
naturally isomorphic to the space of weak Poisson brackets. The last fact
allows one to establish a direct link between the path-integral quantization of
general not necessarily variational dynamics by means of Lagrange structures
and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde
Lagrange Anchor for Bargmann-Wigner equations
A Poincare invariant Lagrange anchor is found for the non-Lagrangian
relativistic wave equations of Bargmann and Wigner describing free massless
fields of spin s > 1/2 in four-dimensional Minkowski space. By making use of
this Lagrange anchor, we assign a symmetry to each conservation law.Comment: A contribution to Proceedings of the XXXI Workshop on the Geometric
Methods in Physic
Classical and quantum stability of higher-derivative dynamics
We observe that a wide class of higher-derivative systems admits a bounded
integral of motion that ensures the classical stability of dynamics, while the
canonical energy is unbounded. We use the concept of a Lagrange anchor to
demonstrate that the bounded integral of motion is connected with the
time-translation invariance. A procedure is suggested for switching on
interactions in free higher-derivative systems without breaking their
stability. We also demonstrate the quantization technique that keeps the
higher-derivative dynamics stable at quantum level. The general construction is
illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative
scalar field model, and the Podolsky electrodynamics. For all these models, the
positive integrals of motion are explicitly constructed and the interactions
are included such that keep the system stable.Comment: 39 pages, minor corrections, references adde
Multi-Hamiltonian formulations and stability of higher-derivative extensions of Chern-Simons
Most general third-order linear gauge vector field theory is considered.
The field equations involve, besides the mass, two dimensionless constant
parameters. The theory admits two-parameter series of conserved tensors with
the canonical energy-momentum being a particular representative of the series.
For a certain range of the model parameters, the series of conserved tensors
include bounded quantities. This makes the dynamics classically stable, though
the canonical energy is unbounded in all the instances. The free third-order
equations are shown to admit constrained multi-Hamiltonian form with the
zero-zero components of conserved tensors playing the roles of corresponding
Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's
one, which is unbounded. The Hamiltonian formulations with different
Hamiltonians are not connected by canonical transformations. This means, the
theory admits inequivalent quantizations at the free level. Covariant
interactions are included with spinor fields such that the higher-derivative
dynamics remains stable at interacting level if the bounded conserved quantity
exists in the free theory. In the first-order formalism, the interacting theory
remains Hamiltonian and therefore it admits quantization, though the vertices
are not necessarily Lagrangian in the third-order field equations.Comment: 19 page
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