BRST analysis of general mechanical systems

Abstract

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.

38 pages, misprints corrected, references and the Conclusion added

References in corpus (7)

• A Poincare lemma for sigma models of AKSZ type
• First order parent formulation for generic gauge field theories
• Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory
• Schwinger-Dyson equation for non-Lagrangian field theory
• Quantizing non-Lagrangian gauge theories: an augmentation method
• Local BRST cohomology in (non-)Lagrangian field theory
• Normal forms and gauge symmetries of local dynamics

Cited by in corpus (13)

• Classical and quantum stability of higher-derivative dynamics
• Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• Gauge PDE and AKSZ-type Sigma Models
• Conservation Laws and Stability of Field Theories of Derived Type
• Peierls brackets in non-Lagrangian field theory
• Higher time-derivative theories from space-time interchanged integrable field theories
• Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
• Third order extensions of $3d$ Chern-Simons interacting to gravity: Hamiltonian formalism and stability
• Integrable scattering theory with higher derivative Hamiltonians
• Nonlinear evolution of disturbances in higher time-derivative theories
• Quantisations of exactly solvable ghostly models
• Extended Chern-Simons model for a vector multiplet