Quark trapping for lattice U(1) gauge fields

We show for lattice U(1) gauge fields in d = 3 dimensions, that 〈exp(i∮_CAdx)〉 ? exp (? const.T lnL), where C is a rectangle of dimension T × L, T ? L. This indicates quark trapping, by a potential at least as strong as Coulomb.     

The supersymmetric Wess-Zumino action and U(1) gauge fields

The supersymmetric effective action is constructed which when varied under gauge groups containing explicit U(1) factors reproduces the mixed gauge field contribution to the SU(N) anomaly while being U(1) invariant. It constitutes generalization of the supersymmetric Wess-Zumino action. The form of supersymmetric mixed anomaly is also discussed.     

Phase structure of a U(1) lattice gauge theory with dual gauge fields

We introduce a U(1) lattice gauge theory with dual gauge fields and study its phase structure. This system is partly motivated by unconventional superconductors like extended s-wave and d  -wave superconductors in the strongly-correlated electron systems and also studies of the t–J$t\text{–}J$ model in the slave-particle representation. In this theory, the “Cooper-pair” (or RVB spinon-pair) field is put on links of a cubic lattice due to strong on-site repulsion between original electrons in contrast to the ordinary s  -wave pair field on sites. This pair field behaves as a gauge field dual to the U(1) gauge field coupled with the hopping of electrons or quasi-particles of the t–J$t\text{–}J$ model, holons and spinons. By Monte Carlo simulations we study this lattice gauge model and find a first-order phase transition from the normal state to the Higgs (superconducting) phase. Each gauge field works as a Higgs field for the other gauge field. This mechanism requires no scalar fields in contrast to the ordinary Higgs mechanism. An explicit microscopic model is introduced, the low-energy effective theory of which is viewed as a special case of the present model.     

Quantum quark processes in uniform non-Abelian gauge fields. Quark propagators

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 65–69, July, 1991.     

Deconfinement transition in three-dimensional compact U(1) gauge theories coupled to matter fields

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This follows from a nontrivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge fields, which form a gas of magnetic monopoles. For logarithmic interactions, the original electric charges are unconfined. The confined phase, which is permanent in the absence of matter fields, is reached at a critical electric charge, where the interaction between magnetic charges is screened by a pair-unbinding in a Kosterlitz-Thouless-like phase transition.     

Characteristic numbers of U1-valued lattice gauge fields

If a U₁-valued latice gauge field u defined on a periodic, 2-dimensional lattice satisfies the generic continuity condition uuuu ≠ − 1, it can be used to construct a principal U₁-bundle over the torus and in that bundle a connection such that parallel transport along bonds is given by u. In higher dimensions this construction can only be carried out if u is monopole-free (otherwise no such bundle can exist). The characteristic classes and numbers of this bundle can then be calculated from u in a straightforward way. Examples are given of u's with maximum possible characteristic numbers, along with a discussion of the behavior of u and of its topology under an action-decreasing deformation.     

Monte Carlo study of U(1) and SU(2) gauge fields on four-dimensional random lattices

The asymptotic behavior of the random lattice gauge model is examined. Numerical results of the specific heat of U(1) and SU(2) on the random lattices of a different number of sites in four dimensions are reported and the phase structure is discussed.     

Universal properties of U(1) gauge theories

The previously known analogies between four-dimensional compact U(1) lattice gauge theories and the two-dimensional planar model are extended to a number of other results. We show that the monopoles in the gauge theory renormalize the coupling constant α by an amount proportional to the susceptibility of the monopole gas. Confinement occurs when this susceptibility diverges. We argue that α is analogous to the critical exponent η of the planar model, and that the transition occurs at a universal critical value α_c.We also define an analogue of the superfluid density for the gauge theory, in terms of the dependence of the free energy on the boundary conditions, and show that it is universally related to α. Finally, we show that the same physics emerges from a continuum U(1) theory with real magnetic monopoles.     

SU(2)×U(1) gauge gravity

We propose a Lorentz-covariant Yang-Mills “spin-gauge” theory, where the function-valued Pauli matrices play the role of a nonscalar Higgs field. As symmetry group we choose SU(2) × U(1) of the 2-spinors describing particle/antiparticle states. After symmetry breaking, a nonscalar Lorentz-covariant Higgsfield gravity appears, which can be interpreted within a classical limit as Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version.     

U(1) gauge theory on a torus

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. As the lattice spacing approaches zero, provided the coupling constant correspondingly approaches zero, the naturally chosen correlation functions converge to the correlation functions of theR-gauge electrodynamics on three- and four-dimensional torus. When the torus radius tends to infinity these correlation functions converge to the correlation functions of theR-gauge Euclidean electrodynamics.Supported by the Russian Foundation of Fundamental Researches under Grant 93-011-147     

U(1) gauge theory of the quantum hall effect

The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.     

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.     

On gauge invariance of Breit-Wigner propagators

We present an approach to bosonic (Z ^o,W ^±) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for theZ ^o-boson propagator we extend previous analyses and show that the part proportional tok k _v /M ² must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.     

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.