Seminario
" Quantization of Constrained Systems"
Relatore: Prof. John R. Klauder Note: Le lezioni seguono lo stesso orario nei giorni 31.3, 6.4, 7.4
Aula Newton
06 Aprile 2011 ore 15.30
Abstract

1. Classical constrained systems, 1st and 2nd class systems, reducible and
irregular constraints; Standard quantization approaches (Dirac, FaddeevPopov,
BRST, etc.); quantize first, reduce second; deficiencies in the usual
approaches.
1. Classical constrained systems, 1st and 2nd class systems, reducible and
irregular constraints; Standard quantization approaches (Dirac, FaddeevPopov,
BRST, etc.); quantize first, reduce second; deficiencies in the usual
approaches.
2. Coherent states, reproducing kernel Hilbert spaces; Projection operator
method; Examples: J^2, P^2 +Q^2, P; reducible and irregular constraints:
Q^2+Q^2, Q^{2\Omega}; other examples; observables [O,E] = 0 ; advanced examples
3. Realization of E (universal formula); dynamics with [H,E]\not=0, general
formula; speical case [H,E] = 0. Path integral ; coherent state
path integral ; Wiener measure regularized expression.
4. application to quantum gravity, affine commutation relations; affine coherent
states; choose \eta> to find <\pi'',,g'' ... \pi',g.> in original Hilbert
space; constraints via POM; continuoustime regularization functional integral
including E.


