Introduction to lattice gauge theory

Conference · Thu Jan 01 00:00:00 EST 1987

OSTI ID:5235211

Gupta, R

The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/..cap alpha.., where ..cap alpha.. is the lattice spacing. The continuum (physical) behavior is recovered in the limit ..cap alpha.. ..-->.. 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5235211
• Report Number(s): LA-UR-88-629; CONF-8707141-5; ON: DE88006073
• Resource Relation: Conference: Theoretical advanced summer institute, Santa Fe, NM, USA, 6 Jul 1987
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
COMPUTERIZED SIMULATION
QUANTUM MECHANICS
STATISTICAL MECHANICS
CORRELATION FUNCTIONS
EXPECTATION VALUE
FERMIONS
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GLUEBALLS
HAMILTONIANS
HARMONIC OSCILLATORS
HIGGS MODEL
MONTE CARLO METHOD
PARTITION FUNCTIONS
QUANTUM CHROMODYNAMICS
TOPONIUM
BOSONS
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
EQUIPMENT
FIELD THEORIES
FUNCTIONS
HADRONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
MESONS
OSCILLATORS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARKONIUM
SIMULATION
645400* - High Energy Physics- Field Theory