Non-Abelian gauge theory on a finite-element lattice

Journal Article · Wed Feb 14 23:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.1261· OSTI ID:6965064

Milton, K A ^[1]; Grose, T ^[2]

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1. Department of Physics, The Ohio State University, Columbus, Ohio 43210 (USA) Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019 (USA)
2. Department of Physics Department of Astronomy, The University of Oklahoma, Norman, Oklahoma 73019 (USA)

We formulate the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice. This is done by a straightforward iterative approach, in which successive interaction terms are added to the Dirac and Yang-Mills equations of motion, and to the field strength, in order to preserve gauge invariance, yielding a series in powers of {ital ghA}. Here {ital g} is the coupling constant, {ital h} is the lattice spacing, and {ital A} is the gauge potential. A simple, nonlocal, iterative formula is obtained for the interaction terms in the equations of motion. Difference equations which are satisfied by the full interaction terms are derived. On the other hand, the field strength is expressed locally in terms of the potential, in terms of nested commutators. The transformations of the gauge potentials are similarly determined to be series of nested commutators.

• OSTI ID: 6965064
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:4; ISSN 0556-2821; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
EQUATIONS OF MOTION
FERMIONS
FIELD EQUATIONS
FIELD THEORIES
FINITE ELEMENT METHOD
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
ITERATIVE METHODS
LATTICE FIELD THEORY
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
SINE-GORDON EQUATION
VECTOR FIELDS
WAVE EQUATIONS
YANG-MILLS THEORY