Group averaging in the (p,q) oscillator representation of SL(2,R)

Details Group averaging in the (p,q) oscillator representation of SL(2,R) Group averaging in the (p,q) oscillator representation of SL(2,R)

2003-12-02

arxiv.org/abs/gr-qc/0312014v2

J.Math.Phys. 45 (2004) 1919-1943

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages. LaTeX with amsfonts, amsmath, amssymb. (References added; minor typos corrected.)

Scientific paper

We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a distinguished o(p,q) observable algebra. The gauge group of the quantum theory is the double cover of SL(2,R), and its representation on the auxiliary Hilbert space is isomorphic to the (p,q) oscillator representation. When p>1, q>1 and p+q == 0 (mod 2), we obtain a physical Hilbert space with a nontrivial representation of the o(p,q) quantum observable algebra. For p=q=1, the system provides the first example known to us where group averaging converges to an indefinite sesquilinear form.

Affiliated with

Also associated with

No associations

Rating

Group averaging in the (p,q) oscillator representation of SL(2,R) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Group averaging in the (p,q) oscillator representation of SL(2,R), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Group averaging in the (p,q) oscillator representation of SL(2,R) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687825