non-Abelian Lattice Gauge Theories Research Articles

Boundary effects in the Monte Carlo calculations of lattice gauge theories

The effect of the boundary conditions in the Monte Carlo calculations of non-abelian lattice gauge theories are studied by performing the calculations with the boundary conditions varied.

The spherical model as a guide to specific heat phase transitions

We investigate numerically and analytically the behaviour of the specific heat in the spherical model in d = 3,4,5,6,7 and ∞ with a view to learning about phase transitions evidenced by anomalous behaviour in the specific heat. The specific heat is finite but its derivative is discontinuous or singular, and for d ⩾ 5 there is a finite discontinuity in the specific heat itself. Possible similarities with non-abelian lattice gauge theories are discussed especially in the light of recent Monte Carlo studies of the specific heat.

Towards the phase structure of euclidean lattice gauge theories with fermions

We propose the phase structure of abelian and non-abelian lattice gauge theories with fermions. We especially analyse Wilson's lattice action with euclidean discrete space-time. We mainly analyse 〈 ψ nψ n〉 as an order parameter for the fermion-gauge coupled system. The Wilson loop integral and plaquette-plaquette two-point function are also useful in working out abelian phase diagrams. We will discuss physical implications of the phase diagrams, especially for the mass spectrum in the lattice continuum limit and chiral symmetry breaking. The 1/ N expansion and a random walk idea are used in the formulation and play an important role in computing meson and baryon propagators in the strong coupling limit.

Small coupling (low temperature) expansions of nonabelian Yang-Mills fields on a lattice in temporal gauge

A systematic approach to large β expansions of nonabelian lattice gauge theories in temporal gauge is developed. The gauge fields are parameterized by a particular set of coordinates. The main problem is to define a regularization scheme for the infrared singularity that in this gauge appears in the Green's function in the infinite lattice limit. Comparison with exactly solvable two-dimensional models proves that regularization by subtraction of a naive translation invariant Green's function does not work. It suggests to use a Green's function of a half-space lattice first, to place the local observable in this lattice, and to let its distance from the lattice boundary tend to infinity at the end. This program is applied to the Wilson loop correlation function for the gauge group SU(2) which is calculated to second order in 1 β .

On the roughening transition in non-abelian lattice gauge theories

We estimate the location β R = ( g R 2 N) −1 of the recently discussed roughening transition for SU( N) lattice gauge theories in ν = 3 and 4 dimensions. The obtained values always lie in the crossover region where the string tension starts to deviate significantly from the leading strong coupling behaviour. β R( N) increases as N increases, tending to a finite limit (≈0.38 for ν = 4) as N → ∞. Results for the solid on solid model (SOS) approximation are also presented and shown to give a good qualitative description; however, group theoretical effects seem to be important for quantitative estimates.

Phase structure of non-Abelian lattice gauge theories

The phase structure of four-dimensional lattice gauge theories based on finite non-Abelian groups is studied by Monte Carlo computations. All models examined exhibit a two-phase structure with a first-order phase transition. In three systems where the gauge group is a discrete subgroup of SU(2) the critical temperature moves toward zero as the order of the group increases and the high-temperature phase has confining properties.

Multiple vacua for non-abelian lattice gauge theories

The various formulations of gauge theories characterized by the parameter θ are constructed for the lattice version of these theories. We do not rely on the existence of topologically stable solutions of the classical equations. These constructions are based on the existence of inequivalent representations of the canonical commutation relations.

Effective Actions in Lattice Gauge Theories

Effective coupling constants of non-Abelian lattice gauge theories are calculated when actions on each cell are small. The recursion equation for the effective coupling constant 9err(t) shows that Qerr(t) increases exponentially in the infrared region. This behavior is also obtained from the law of area due to Wilson. An existence of fixed points in QED is also suggested. In our opinion there have so far been no methods appropriate for the estimation. Migdal's recursion equation can be numerically solved only on a computer, even in the strong coupling region. We propose here a simple recursion formula for the effective coupling constant, which is easily derived by analytic methods and is valid well in the strong coupling region. Our investigation is unsatisfactory in the sense that it cannot say anything about the asymptotic freedom in the ultraviolet region, but in the infrared region our formula will be quite satisfactory. First we derive in § 2 the effective coupling formula from the direct calculation of the effective action. In § 3 this formula is shown to be derived also from the law of area. An existence of fixed points in QED is also suggested.

Composite hadrons in non-Abelian lattice gauge theories

Euclidean non-Abelian gauge theories are quantized on a (finite) lattice using functional integration. From the general from of the 2 m-point Schwinger function for the fundamental fermions fields, dynamical consequences for composite meson and fermion fields are investigated. The Okubo-Zweig-Iizuka rule is derived and an analogy to non-relativistic potentials for the quark-antiquark and the 3-quark system is exhibited.