Phase transition ofSU(3) gauge theory at finite temperature

We present evidence for the presence of a phase transition inSU(3) lattice gauge theory at finite temperature using Monte-Carlo methods. An extrapolation to the continuum limit leads to the valueT _c =Λ_mom±15% for the critical temperature separating the two phases.     

Geometry of gauge fields for extended objects

A geometric interpretation of gauge field for extended objects is given. This interpretation is a generalization of the interpretation of electrodynamics based on connections in principal fibre bundles. Only the geometry of gauge fields is formulated. Field dynamics and interaction of the fields with extended objects will be studied separately.     

Geometry of gauge fields in a multidimensional universe

Let S be a group of automorphisms of a principal fibre bundle (U, , E, R), both groups S and R being compact. Let I (resp. H) be the isotropy group of S (resp. S x R) acting on E (resp. U), and let N(I) (resp. N(H)) be the normalizer of I (resp. H) in S (resp. S x R). We construct two principal bundles P(M, N(I)|I) E and Q(M, N(H)|H) U, where M=E/S is the space of orbits of S in E, and we prove that, given a connection A in P, there is a one-to-one correspondence between S-invariant connections in U and triples (B, , ), where B is a connection in Q, part of which is a pullback ^* A of A, and , are scalars which are crosssections of certain vector bundles associated with Q. The resulting final gauge group N(H)|H is shown to contain as a normal subgroup the centralizer of I in R, known from earlier works of other authors. A dimensional reduction of the Einstein-Yang-Mills system on E is briefly discussed.Partially supported by the Polish Ministry of Science, Higher Education and Technology under the Project MRI-7.     

Self-dualSU(N) gauge fields

We give a method by which we can construct solutions to the self-dualSU(N) gauge field equations, some of which can be chosen as seed solutions.     

Variational calculation of SU(2) quantum gauge fields

The SU(2) Yang-Mills quantum field is studied by Coulomb-gauge continuum-hamiltonian methods using a variational approximation. The field amplitudes are represented by a truncated momentum expansion in the spatial domain S³. The calculations support Gribov's scenario for the generation of a mass gap in the spectrum of physical states and the confinement of color.     

Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories II:SU (3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0⁺⁺, 2⁺⁺, 0^?+ and, most interestingly from the experimental point of view, the oddball 1^?+. We calculate the 0⁺⁺ and 2⁺⁺ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.     

Self-duality equations for spherically symmetric SU(2) gauge fields

A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that the SU(2) gauge model is self-dual on a Schwarzschild space-time but not on a Reissner-Nordstr?m one. Received: 24 May 2002 / Accepted: 1 July 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: gzet@phys.tuiasi.ro Communicated by A. Sch?fer     

An approach to SU(2) gauge fields in Minkowski space-time

A reparametrization-invariant formulation of SU(2) gauge theory in Minkowski space-time is given in terms of differential forms. A map of space-time into a compact region is used and the SU(2) Maurer-Cartan forms employed to establish a convenient gauge. New solutions to the theory are presented and discussed.     

Topological charge of (lattice) gauge fields

Using recently derived explicit formulae for the 2- and 3-cochains in SU(2) gauge theory, we are able to integrate the Chern-Simons density analytically. We arrive — in SU(2) — at a local algebraic expression for the topological charge, which is the sum of local winding numbers associated with the corners (lattice points) of the cells covering the manifold plus contributions from possible isolated gauge singularities which manifest themselves as “vortices” in the 1-, 2- or 3-cochains. Among others we consider hypercubic geometry — i.e. covering the manifold by hypercubes — which is of particular interest to lattice Monte Carlo applications. Finally, we extend our results to SU(3) gauge theory.     

Coupling of gravity to matter viaSO(3, 2) gauge fields

We consider gravity from the quantum field theory point of view and introduce a natural way of coupling gravity to matter by following the gauge principle for particle interactions. The energy-momentum tensor for the matter fields is shown to be conserved and follows as a consequence of the dynamics in a spontaneously brokenSO(3, 2) gauge theory of gravity. All known interactions are described by the gauge principle at the microscopic level.     

SU(N) gauge fields with spherical symmetry

A method to construct spherically symmetricSU(N) gauge fields and an invariant classification are presented. For the groupSU(3) the ansätze are completely elaborated. The corresponding sourcelessSU(3)-Yang-Mills equations are discussed.     

Renormalized finite temperature effective potential ofSU(2) Yang-Mills theory

It is shown that the renormalized finite temperature effective potential for continuumSU(2) Yang-Mills theory develops a non-perturbative minimum for sufficiently strong coupling, i.e. below a critical temperature. The corresponding phase can be the candidate for the confining phase of the continuum theory and becomes energetically favoured basicly due to the decay of theA ⁰ condensate into three gluons.     

Simple construction ofSU(3) representations using theSU(2) projection technique

SU(3) representations for theSU(3) SU(2) chain are constructed in a new way usingSU(2) projection operators. TheSU(3) D-functions, presented in new parametrizations, are expressed in terms ofSU(2) D-functions and 6j-symbols.Valuable discussions with Dr. J. Niederle are gratefully acknowledged.     

Unitary irreducible representations ofSU(2,2)

Using a Lie algebra method based on works byHarish-Chandra, several series of unitary, irreducible representations of the groupSU(2,2) are obtained.     

Spin waves and dual spin waves ofSU(2) chiral models

We study the low coupling (low temperature) limit of the dual versions of chiralSU(2) invariant models. Based on a conjecture of Regge about the asymptotic behaviour of the mean square of 3nj-coefficients forj→∞, we show that the low coupling excitations of the dual chiral models are vibrational modes of a triangular manifold, which is embedded in Euclidean three dimensional space and is formed by classical angular momenta.     

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.     

Transcendent self-dual solutions for SU(2) gauge fields on euclidean four-dimensional space

By applying the method of separation of variables, we find a particular class of solutions of Yang's equations in the R-gauge for self-dual SU(2) static, axisymmetric gauge fields on euclidean four-dimensional flat space. The solutions obtained are depending functionally on a particular form of the fifth Painlevé transcendent.