Gauge Invariance and Weyl-polymer Quantization by Franco Strocchi

Author:Franco Strocchi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The gauge transformations

leave the canonical structure and the Hamiltonian invariant, but irreducible representations π of are obtained by fixing the gauge, namely by fixing the value of the non-trivial center of , generated by e i2π p , namely , . In the following, for simplicity, we shall take . The following group of gauge transformations (hereafter called large gauge transformations)

(3.4.3)

survive the gauge fixing and are implemented by the unitary operators

(3.4.4)

The exponential field algebra contains a gauge invariant subalgebra , with the physical interpretation of observable algebra, generated by the gauge invariant variables , , E. has a non-trivial center , generated by the periodic variable , equivalently by T; hence, the irreducible representations of are labeled by the points , , of the spectrum of T; the corresponding Hilbert spaces are called sectors.

The Hamiltonian takes a simple form in terms of the new canonical variables , e i q , and p:

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