Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions

Details Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions

1993-12-07

arxiv.org/abs/gr-qc/9312013v1

Class.Quant.Grav.11:1615-1630,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTeX, 1 postscript figure included, uses epsf.sty, G\"oteborg ITP 93-39

Scientific paper

10.1088/0264-9381/11/7/005

We consider the phase-space of Yang-Mills on a cylindrical space-time ($S^1 \times {\bf R}$) and the associated algebra of gauge-invariant functions, the $T$-variables. We solve the Mandelstam identities both classically and quantum-mechanically by considering the $T$-variables as functions of the eigenvalues of the holonomy and their associated momenta. It is shown that there are two inequivalent representations of the quantum $T$-algebra. Then we compare this reduced phase space approach to Dirac quantization and find it to give essentially equivalent results. We proceed to define a loop representation in each of these two cases. One of these loop representations (for $N=2$) is more or less equivalent to the usual loop representation.

Affiliated with

Also associated with

No associations

Rating

Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions 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 Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-311899