Alex C. Kalloniatis

Confinement and chiral symmetry breaking via domain - like structures in the QCD vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.

Zero modes and the vacuum problem: A study of scalar adjoint matter in two-dimensional Yang-Mills theory via light-cone quantization.

SU(2) Yang-Mills theory coupled to massive adjoint scalar matter is studied in 1+1 dimensions using discretized light-cone quantization. This theory can be obtained from pure Yang-Mills theory in 2+1 dimensions via dimensional reduction. On the light cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum-mechanical potential governing the dynamical gauge mode. Because of a condensation of the lowest momentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory, however, the barrier height appears too small to make any impact in this model. Although the theory is superrenormalizable on naive power-counting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The solution of this problem is discussed. {copyright} {ital 1996 The American Physical Society.}

QED(1+1) at finite temperature — a study with light-cone quantisation

Abstract We explore quantum electrodynamics in (1+1) dimensions at finite temperature using the method of Discretized Light-Cone Quantisation (DLCQ). The partition function, energy and specific heat are computed in the canonical ensemble using the spectrum of invariant masses computed with a standard DLCQ numerical routine. In particular, the specific heat exhibits a peak which grows as the continuum limit is numerically approached. A critical exponent is tentatively extracted. The surprising result is that the density of states contains significant finite size artifacts even for a relatively high harmonic resolution. These and the other outstanding problems in the present calculation are discussed.

Light-front QCD(1+1) coupled to adjoint scalar matter

Abstract We consider adjoint scalar matter coupled to QCD(1+1) in light-cone quantization on a finite ‘interval’ with periodic boundary conditions. We work with the gauge group SU(2) which is modified to SU(2) Z 2 by the non-trivial topology. The model is interesting for various nonperturbative approaches because it is the sector of zero transverse momentum gluons of pure glue QCD(2+1), where the scalar field is the remnant of the transverse gluon component. We use the Hamiltonian formalism in the gauge ∂ − A + = 0. What survives in the dynamical zero mode of A + , which in other theories gives topological structure and degenerate vacua. With a point-splitting regularization designed to preserve symmetry under large gauge transformations, an extra A + dependent term appears in the current J + . This is reminiscent of an (unwanted) anomaly. In particular, the gauge invariant charge and the similarly regulated P + no longer commute with the Hamiltonian. We show that nonetheless one can construct physical states of definite momentum which are not invariant under large gauge transformations but do transform in a well-defined way. As well, in the physical subspace we recover vanishing expectation values of the commutators between the gauge invariant charge, momentum and Hamiltonian operators. It is argued that in this theory the vacuum is nonetheless trivial and the spectrum is consistent with the results of others who have treated the large N , SU( N ), version of this theory in the continuum limit.

Quantum electrodynamics in the light-front Weyl gauge.

We examine (3+1)-dimensional QED quantized in the {open_quote}{open_quote}front form{close_quote}{close_quote} with finite {open_quote}{open_quote}volume{close_quote}{close_quote} regularization, namely, in discretized light-cone quantization. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge {ital A}{sup {minus}}=0. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply {open_quote}{open_quote}quantum-mechanical gauge fixing{close_quote}{close_quote} to implement Gauss{close_quote} law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely, displacements. On the light cone the symmetry manifests itself quite differently. {copyright} {ital 1996 The American Physical Society.}

Chirality of quark modes

A model for the QCD vacuum based on a domainlike structured background gluon field with definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological susceptibility and indications that chiral symmetry is spontaneously broken. In this paper we study in detail the eigenvalue problem for the Dirac operator in such a gluon mean field. A study of the local chirality parameter shows that the lowest nonzero eigenmodes possess a definite mean chirality correlated with the duality of a given domain. A probability distribution of the local chirality qualitatively reproduces histograms seen in lattice simulations.

Constituent quark picture out of QCD in two-dimensions — on the light cone

Abstract Using DLCQ as a non-perturbative method, we test Fock-space truncations in QCD1+1 by studying the mass spectra of hadrons in colour SU(2) and SU(3) at finite harmonic resolution K. We include q q q q states for mesons and up to qqqq q states for baryons. With this truncation, we give “predictions” for the masses of the first five states where finite K effects are minimal.