Refined algebraic quantization in the oscillator representation of SL(2,R)
Jul, 199931 pages
Published in:
- J.Math.Phys. 41 (2000) 132-155
e-Print:
- gr-qc/9907004 [gr-qc]
DOI:
Report number:
- AEI-1999-010
View in:
Citations per year
Abstract: (arXiv)
We investigate Refined Algebraic Quantization (RAQ) with group averaging in a constrained Hamiltonian system with unreduced phase space T^*R^4 and gauge group SL(2,R). The reduced phase space M is connected and contains four mutually disconnected `regular' sectors with topology R x S^1, but these sectors are connected to each other through an exceptional set where M is not a manifold and where M has non-Hausdorff topology. The RAQ physical Hilbert space H_{phys} decomposes as H_{phys} = (direct sum of) H_i, where the four subspaces H_i naturally correspond to the four regular sectors of M. The RAQ observable algebra A_{obs}, represented on H_{phys}, contains natural subalgebras represented on each H_i. The group averaging takes place in the oscillator representation of SL(2,R) on L^2(R^{2,2}), and ensuring convergence requires a subtle choice for the test state space: the classical analogue of this choice is to excise from M the exceptional set while nevertheless retaining information about the connections between the regular sectors. A quantum theory with the Hilbert space H_{phys} and a finitely-generated observable subalgebra of A_{obs} is recovered through both Ashtekar's Algebraic Quantization and Isham's group theoretic quantization.- mechanics: classical
- quantization
- Hamiltonian formalism
- operator: algebra
- gauge field theory: SL(2,R)
References(0)
Figures(0)
Loading ...