Gauge theories and neutral currents

We consider neutral current effects in some gauge theoretic models of weak and electromagnetic interactions. Asymptotic invariance under the gauge group is proposed and used for estimating deep-inelastic cross sections. Our analysis underlines the need for a systematic search for hadronic threshold effects in the coupling of neutral currents.     

Canonical and D-transformations in theories with constraints

We describe a class of transformations in a super phase space (we call them D-transformations) which play the role of ordinary canonical transformations in theories with second-class constraints. Namely, in such theories they preserve the form invariance of equations of motion, their quantum analogs are unitary transformations, and the measure of integration in the corresponding Hamiltonian path integral is invariant under these transformations.     

Gauge theories with minimal subtraction and the decoupling theorem

We show explicitly, to the two-loop level, that the decoupling theorem of Appelquist and Carazzone is valid, and a consistent light effective field theory exists, for quantum electrodynamics in arbitrary α-gauges, and non-abelian gauge theory in α = 0, Landau gauge, renormalized by minimal subtraction.     

Gauge theories with strong coupling in four dimensions

The long distance behavior of singlet current correlation functions of gauge theories on a lattice are found approximately using the renormalization group. For strong coupling the behavior is similar to that found in the lattice massive Schwinger model.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Gauge theories,instantons and algebraic geometry

We review the definition of instanton (= pseudoparticle) solutions and their importance in the context of nonabelian gauge (= Yang-Mills) theories, as well as the recent progress, due to Atiyah and Ward, in their construction, using the Penrose twistor transform and methods of algebraic geometry. In particular, we present a proof of the theorem of Atiyah and Ward on the correspondence between SU(2) instanton solutions over the 4-sphere and certain algebraic 2-dimensional complex vector bundles over complex projective 3-space.     

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.     

Gauge theories with imaginary chemical potential and the phases of QCD

The phase structure of gauge theories with fermions as a function of imaginary chemical potential is related to the confining properties of the theory. It is controlled by a remnant of the Z_N which is present in the absence of fermions. At high temperature the theory has a first-order phase transition as a function of imaginary chemical potential . This transition is expected to be absent in the low-temperature phase. Monte Carlo simulations are proposed which would check these ideas. It is shown that properties of the theory at nonzero fermion density can be deduced from its behavior at finite imaginary chemical potential.     

Canonical formalism of gauge theories with reducible constraints

A procedure for the canonical quantization of gauge theories with reducible constraints (that is, linearly dependent) is proposed. The procedure consists of extending the initial phase space and filling out the initial system of constraints to an aggregate of linearly indepndent constraints. The equivalence is shown between the proposed quantization scheme and canonical quantization when only the linearly independent constraints are chosen from the initial system of constraints.Translated from Izvestiya Vysshikh.Uchebnykh Zavedenii, Fizika, No. 7, pp. 64–68, July, 1985.     

Gauge theories, vertex models, and quantum groups

It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable “vertex models” of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional “duality”, why this must be so.     

Gauge invariants and Killing tensors in higher-spin gauge theories

In free completely symmetric tensor gauge field theories on Minkowski space–time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.     

Gauge theories,black hole evaporation and cosmic censorship

Recent work of Linde, which suggests that gauge theories modify the effective gravitational constant, are applied to the theory of black hole evaporation. Considerable modification of the late stages of evaporation are predicted. Contrary to expectations, the black hole never attains a sufficient temperature to enter the “antigravity” regime, which would represent a failure of cosmic censorship.