Lattice gauge theory approach to quantum chromodynamics
The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory are discussed. A simple dielectric model of confinement is considered as an intuitive guide to the vacuum of non-Abelian gauge theories. Next, the Euclidean form of lattice gauge theory is introduced, and an assortment of calculational methods are reviewed. These include high-temperature expansions, duality, Monte Carlo computer simulations, and weak coupling expansions. A ..lambda..-parameter calculation for asymptotically free-spin models is presented. The Hamiltonian formulation of lattice gauge theory is presented and is illustrated in the context of flux tube dynamics. Roughening transitions, Casimir forces, and the restoration of rotational symmetry are discussed. Mechanisms of confinement in lattice theories are illustrated in the two-dimensional electrodynamics of the planar model and the U(1) gauge theory in four dimensions. Generalized actions for SU(2) gauge theories and the relevance of monopoles and strings to crossover phenomena are considered. A brief discussion of the continuity of fields and topologial charge in asymptotically free lattice models is presented. The final major topic of this review concerns lattice fermions. The species doubling problem and its relation to chiral symmetry are illustrated. Staggered Euclidean fermion methods are discussed in detail, with an emphasis on species counting, remnants of chiral symmetry, Block spin variables, and the axial anomaly. Numerical methods for including fermions in computer simulations are considered. Jacobi and Gauss-Siedel inversion methods to obtain the fermion propagator in a background gauge field are reviewed.
- Research Organization:
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801
- OSTI ID:
- 5827300
- Journal Information:
- Rev. Mod. Phys.; (United States), Vol. 55:3
- Country of Publication:
- United States
- Language:
- English
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LATTICE FIELD THEORY
GAUGE INVARIANCE
QUANTUM CHROMODYNAMICS
CHIRAL SYMMETRY
DUALITY
FERMIONS
HAMILTONIANS
MAGNETIC MONOPOLES
MONTE CARLO METHOD
PERTURBATION THEORY
QUARK MODEL
RENORMALIZATION
REVIEWS
SYMMETRY BREAKING
COMPOSITE MODELS
DOCUMENT TYPES
ELEMENTARY PARTICLES
FIELD THEORIES
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MONOPOLES
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SYMMETRY
645400* - High Energy Physics- Field Theory
645201 - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory