HAMILTONIAN APPROACH TO Z(N) LATTICE GAUGE THEORIES

Horn, D.; Weinstein, M.; Yankielowicz, S.

doi:10.1103/PhysRevD.19.3715

HAMILTONIAN APPROACH TO Z(N) LATTICE GAUGE THEORIES

1979

55 pages

Published in:

Phys.Rev.D 19 (1979) 3715

DOI:

10.1103/PhysRevD.19.3715

Report number:

TAUP-723-79

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Abstract: (APS)

We develop a Hamiltonian formalism for Z(N) lattice gauge theories. Duality is expressed by algebraic operator relations which are the analog of the interchange of electric and magnetic fields in D=3 space dimensions. In D=2 duality is used to solve the gauge condition. This leads to a generalized Ising Hamiltonian. In D=3 our theory is self-dual. For N→∞ the theory turns into "periodic QED" in appropriate limits. This leads us to propose the existence of three phases for N>Nc≃6. Their physical properties can be classified as electric-confining, nonconfining, and magnetic-confining.

GAUGE FIELD THEORY: LATTICE
GAUGE FIELD THEORY: Z(N)
DUALITY: TRANSFORMATION
QUARK: CONFINEMENT
INVARIANCE: GAUGE
QUANTUM CHROMODYNAMICS
STATISTICAL MECHANICS: ISING
GAUGE FIELD THEORY: TWO-DIMENSIONAL
GAUGE FIELD THEORY: THREE-DIMENSIONAL
GAUGE FIELD THEORY: CRITICAL PHENOMENA

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