Strong-coupling field theories. II. Fermions and gauge fields on a lattice

Journal Article · Wed Sep 15 00:00:00 EDT 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.1627· OSTI ID:7350585

Drell, S D; Weinstein, M; Yankielowicz, S

This paper (the second in a series) reports our recent progress in the study of strong-coupling quantum field theories on a lattice. In particular we study theories involving fermions and gauge fields and pay special attention to the peculiar problems encountered when one formulates theories of fermions on a lattice. It is unique to our approach that we preserve local chiral symmetry and at the same time correctly count the number of fermionic states. We demonstrate how our formalism works with the lattice Thirring and Schwinger models, whose continuum limits are solvable in one space and one time dimension. We show in the strong-coupling limit that these theories are equivalent to a Heisenberg antiferromagnetic chain. We also discuss briefly some general features of non-Abelian gauge theory of quarks and gluons in three space and one time dimension. The most interesting results we have to report at this stage are as follows: (i) The only ''gauge-invariant states'' which remain at low mass in the limit of very strong gauge coupling have the quantum number of physical hadrons. (ii) The resulting ''effective strong-coupling'' theory preserves the full chiral symmetry of the exact theory (SU(3) x SU(3) if we introduce three flavors of quarks each with three colors) and describes a theory of ''massless bare hadrons'' interacting with one another through a quark interchange mechanism of finite strength. (AIP)

• Research Organization: SLAC National Accelerator Lab., Menlo Park, CA (United States)
• OSTI ID: 7350585
• Journal Information: Phys. Rev., D; (United States), Vol. 14:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
STRONG-COUPLING MODEL
CHIRAL SYMMETRY
FERMIONS
GAUGE INVARIANCE
GLUON MODEL
QUARK MODEL
SCHWINGER SOURCE THEORY
SU-3 GROUPS
THIRRING MODEL
COMPOSITE MODELS
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
SU GROUPS
SYMMETRY
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory