Coherent States and the Quantization of (1+1)Dimensional YangMills Theory
Abstract
This paper discusses the canonical quantization of (1+1)dimensional YangMills theory on a spacetime cylinder from the point of view of coherent states, or equivalently, the SegalBargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinitedimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gaugeinvariant subspace, using a suitable regularization procedure. We obtain in this way a new family of ``reduced'' coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized SegalBargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1142/S0129055X0100096X
 arXiv:
 arXiv:quantph/0012050
 Bibcode:
 2001RvMaP..13.1281H
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 Rev. Math. Phys. 13 (2001) 12811306