Nonexistence of finite-energy solutions in some gauge models

A theorem which forbids the existence of certain nontrivial static finite-energy classical solutions to Yang-Mills-Higgs equations in dependence on the spatial dimension is generalized to include fields with nonvanishing electric-like componentsF _0j .Dedicated to 30th anniversary of the Joint Institute for Nuclear Research.     

Disorder solutions for gauge systems

Lattice gauge systems with an exactly computable partition function are presented. These models are analouges of the disorder points of spin systems. They could be used for testing Monte Carlo procedures.     

Extended-natural gauge models and complementarity

We propose a new condition “extended naturalness” which should be satisfied by any physically sensible gauge theory. In order that a theory is extended-natural, all discrete quantities observed in low energies must be stable against variations of discrete parameters of the theory defined in large mass scales. We find that SU(N) gauge models become extended-natural when we choose appropriate fermion representations. Further, if N is a multiple of 8, the models turn out to be good examples of complementary gauge theories.     

Parity violation in left-right symmetric gauge models

The parity violating effective interaction in models based on the SU(2)_L × SU(2)_R × U(1) gauge group is shown to have the same structure, at zero momentum transfer, as in the Weinberg-Salam model, apart from a constant scale factor.     

On neutral currents in two-Z-boson gauge models

A systematic procedure is considered for the phenomenological analysis of neutral current interactions in an arbitrary two-Z-boson gauge model by means of a general neutral current effective Lagrangian. Expressions for two gauge boson masses and their mixing angle have been obtained directly through the effective Lagrangian parameters. A general classification of possible types of two-Z-boson gauge models is presented in accordance with the form of the effective Lagrangian.     

Neutral currents in left-right symmetric gauge models

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2) _L ⊗ SU(2) _R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.     

Cosmological solutions in a spontaneously broken gauge theory

We consider solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically de Sitter space-time. The basic features of two classes of solutions are discussed, one of them corresponding to magnetic monopoles, the other one to sphalerons. We find that although the total mass within the cosmological horizon of these configurations is finite, their mass evaluated at timelike infinity generically diverges for most values of the cosmological constant. Also, no solutions exist in the absence of a Higgs potential.     

Fluxon ratchet potentials in superconducting circuits

A fluxon in a Josephson-junction parallel array behaves like a single particle in a periodic pinning potential. Different configurations of critical currents and cell areas result in different profiles for the fluxon potential. We analyze the minimal conditions to achieve an effective potential in which mirror symmetry is absent, namely a fluxon ratchet potential. Following one of the configurations, we designed circular arrays and probed some of the fluxon properties. Theoretical predictions are nicely fulfilled by the experiments. Received: 20 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Perturbation theory for two-dimensional gauge models

Euclidean symmetric integration, previously proposed for the SU(N) Yang-Mills theory in the limit of large N, is used to study the propagators in the Schwinger model and the massive vector-meson model in two dimensions. The result of summing the perturbation series agrees with the exact solution in each case. Therefore, perturbation theory is here capable of dealing with non-analytic behaviour in the coupling constant.     

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.     

Reduced models and noncommutative gauge theories

A brief review of the relation between reduced models and noncommutative Yang-Mills (NCYM) theory is given. The twisted Eguchi-Kawai model, the mapping onto NCYM, the Morita equivalence, the fundamental matter, the Wilson loops in NCYM, and the D-brane interpretation are considered.     

Generalised actions for lattice gauge models

We consider simple modifications of the conventional Wilson action for lattice gauge theory. An SU(2) action is defined on “plaquettes” of 2×1 links. It is found to possess phase transitions in three- and four-dimensional realisations of the model. A similar model with gauge group Z(2) is also studied, and found to have two phases in three and four dimensions. We discuss the phase structure of Z(N) gauge models in four dimensions with several coupling constants and present phase diagrams for Z(4), Z(5) and Z(6).     

Derivation of soliton quantization in two gauge models

Feynman rules are derived by a path-integral method for gauge theory solitons using as particular examples the Nielsen-Olesen vortex and the 't Hooft-Polyakov-Julia-Zee monopole-dyon. The masses of these solitons are proven to be manifestly renormalizable to one-loop order in the absence of knowledge of exact solitary solutions. This is done using a technique similar to 't Hooft's “background field method”.     

Distribution of zeros in Ising and gauge models

We discuss some features of Ising and gauge systems in the complex temperature plane. The distribution of zeros of the partition function enables one to study critical properties in a way complementary to the methods using real values. Data on small lattices confirm this picture. Nearby complex singularities seem to exhibit a universal behavior which might have some relation with a model of random surfaces.