Dynamical symmetry breaking in lattice gauge theories
We investigate dynamical breaking of chiral symmetry in quantum chromodynamics defined on a spatial lattice. Our formulation respects chiral symmetry by employing a long-range gradient for the fermion field. In the strong-coupling limit all states with non-zero electric flux are at very high energy, so that the set of degenerate ground states is comprised of all fermionic configurations which are color singlets site by site. We derive an effective Hamiltonian for the mesons in perturbation theory about this limit. Color and flavor are shown to be inessential and we consider the U(1) gauge theory with one flavor of four-component fermions. The effective Hamiltonian is then that of an antiferromagnet whose symmetry group is determined by the dimensionality of space. We study this Hamiltonian using block-spin techniques. We first show that if we drop all but nearest-neighbor interactions the resulting SU(4) antiferromagnet realizes some or all of its symmetry generators in Nambu-Goldstone mode. We hypothesize that this physics survives when one breaks the SU(4) with non-nearest-neighbor terms, and we check this for the one-dimensional theory with an explicit block-spin calculation. Our model in that case is the SU(2) flavor Schwinger model, and we demonstrate the appearance of Goldstone bosons corresponding to the axial generators when the vacuum is selected by a mass perturbation. This does not contradict Coleman's theorem because no local operator acquires a vacuum expectation value to break the symmetry. Our hypothesis, thus strengthened, goes on to predict spontaneous breaking of ..gamma../sub 5/ symmetry in three dimensions. We show how the U(1) Goldstone boson might disappear in the continuum limit.
- Research Organization:
- Princeton Univ., NJ (USA)
- OSTI ID:
- 6209885
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
LATTICE FIELD THEORY
SYMMETRY BREAKING
CHIRAL SYMMETRY
FERMIONS
GOLDSTONE BOSONS
HAMILTONIANS
MESONS
QUANTUM CHROMODYNAMICS
SU-2 GROUPS
SU-4 GROUPS
U-1 GROUPS
BOSONS
ELEMENTARY PARTICLES
FIELD THEORIES
HADRONS
LIE GROUPS
MATHEMATICAL OPERATORS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SU GROUPS
SYMMETRY
SYMMETRY GROUPS
U GROUPS
645300* - High Energy Physics- Particle Invariance Principles & Symmetries
645400 - High Energy Physics- Field Theory