nLab Quantization of Gauge Systems

Redirected from "simplicial topological spaces".
Contents

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

\infty-Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Related topics

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

This entry is about the textbook:

on the BRST-BV formalism for describing gauge theories in the generality of constrained Hamiltonian mechanics of field theories deriving from a Lagrangian density.

Contents

1) Constrained Hamiltonian systems

2) Geometry of the constraint surface

3) Gauge invariance of the action

4) Generally covariant systems

5) First-class constraints: further developments

6) Fermi degrees of freedom: classical mechanics over a Grassmann algebra

7) Constrained systems with fermi variables

8) Graded differential algebra – algebraic structure of the BRST symmetry

9) BRST construction in the irreducible case

10) BRST construction in the reducible case

11) Dynamics of the ghosts – gauge-fixed action

12) The BRST transformation in field theory

13) Quantum mechanics of constrained systems: standard operator methods

14) BRST operator method – quantum BRST cohomology

15) Path integral for unconstrained systems

15.1 Path Integral Method of Bose Systems – Basic Feature

15.1.4 Equations of motion – Schwinger-Dyson-Equation

15.5 A first bite at the antifield formalism

15.5.2 Antibracket

15.5.3 Schwinger-Dyson operator

16) Path integral for constrained systems

17) Antifield formalism: classical theory

17.1) Covariant phase space

17.2) Koszul-Tate resolution and longitudinal dd

17.3) BRST symmetry – master equation

17.4) Gauge invariance of the solution of the master equation

18) Antifield formalism and path integral

19) Free Maxwell theory, abelian two-form gauge field

20) Complementary material

category: reference

Last revised on December 23, 2023 at 09:13:10. See the history of this page for a list of all contributions to it.