nLab Quantization of Gauge Systems




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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.


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.