Gravity as Yang-Mills gauge theory

We propose a Yang-Mills field theory of gravity based on a unitary phase-gauge-invariance of the lagrangian where the gauge transformations are those of the SU(2) × U(1) symmetry of the 2-spinors. In the classical limit this microscopic theory results in Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version.     

Spontaneous symmetry breaking of affine field theory

It is possible to construct non-Abelian field theories by gauging Kac-Moody algebras. Here we discuss the spontaneous symmetry breaking of such theories via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra.     

Renormalization group and dynamical symmetry breakdown in abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. We look for solutions which contain non-zero physical masses of the two fermions (m₁, m₂) and of one of the vector bosons (μ) when the bare masses m_1Λ, m_2Λ, μ_Λ approach zero. For a theory without cut-off we obtain results which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant α_Λ of the A_μ vector boson, which remains massless, exceeds some critical value α_c. In this case the fermion masses turn out to be of the superconductivity type.The model's “memory” of the nature of spontaneous symmetry breaking lim_{m1Λ, m2Λ → 0}m_1Λ/m_2Λ ≠ 1 is an indispensible factor for the vector boson to acquire a mass.     

Gravity as a goldstone field in the Lorentz gauge theory

A bundle formalism is applied to interpret the Einstein gravitational field in gauge theory; its topological invariants are discussed.     

Spontaneous breakdown of the gauge chiral symmetry and the cabibbo angle

From the general treatment of the spontaneous breakdown of the chiral SU(3)xSU(3) group down to the electromagnetic U(l) gauge group it is conjectured that the bare Cabibbo angle isπ/4. Imposing the self-consistency condition of Cabibbo and Maiani on the weak and electromagnetic corrections to the chiral symmetry breaking Hamiltonianh=ε₀ u ₀+ +ε₃ u ₃+ε₈ u ₈ leads to the determination of the physical Cabibbo angle. The agreement with the experimental value is reached when the parametrization ofh of Brandt and Preparata is used.     

On the topological reduction from the affine to the orthogonal gauge theory of gravity

Making use of the fibre bundle theory to describe metric–affine gauge theories of gravity we are able to show that metric–affine gauge theory can be reduced to the Riemann–Cartan one. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. Also, a possible framework for the construction of a quantum gravity theory is developed in the text.     

Proof of chiral symmetry breaking in lattice gauge theory

Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.     

On the analogy between superconductivity and chiral symmetry breakdown in the Coulomb gauge

We study spontaneously broken gauge theories which do not explicitly involve boson fields. Our work was motivated by, and justifies, some recent results pointing to a deep analogy between particle physics and superconductivity. Thus we compare in detail the BCS theory of superconductivity, including Coulomb effects, with its relativistic generalization in the Coulomb gauge. The structure of the resulting equations is identical in both cases. The unity is best appreciated in terms of the Schwinger mechanism which leads to plasma oscillations in superconductivity and to massive spin-one particles in the relativistic case. The physical operator densities, such as charge and current densities, differ from those found by other authors concerned with the problem of gauge invariance.     

Dual-BRST symmetry: 6D Abelian 3-form gauge theory

Within the framework of the Becchi–Rouet–Stora–Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.     

Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to $\text{H}\text{=}\text{SU}\text{(3)}{}_{\mathrm{<mtext>C</mtext>}}\text{×}\text{SU}\text{(2)}{}_{\mathrm{<mtext>L</mtext>}}\text{×}\text{U}\text{(1)}{}_{\mathrm{<mtext>R</mtext>}}\text{×}\text{U}\text{(10)}{}_{\mathrm{B?L}}$. For all solutions, the fermions which are chiral with respect to $\text{H}$ form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)_G × U(1)_G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)_G × U(1)_G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.     

Composite operator calculation of chiral symmetry breaking in color gauge theory

In the framework of the formalism of Cornwall et al. for composite operators, we develop a new method for the calculation of the effective potential. We apply the method to the study of chiral symmetry breaking in an SU(N) color gauge theory with n massless flavors and derive analytically the complete effective potential at two fermion loops. We find that in this approximation the theory has two phases: the symmetric phase and the broken phase into the diagonal flavor sub-group.     

Proof of chiral symmetry breaking in strongly coupled lattice gauge theory

We study chiral symmetry in the strong coupling limit of lattice gauge theory with staggered fermions and show rigorously that chiral symmetry is broken spontaneously in massless QED and the gauge-invariant Nambu-Jona-Lasinio model if the dimension of spacetime is at least four. The results for the chiral condensate as a function of the mass imply that the mean-field approximation is an upper bound for this observable which becomes exact as the dimension goes to infinity. For the model with gauge groupU(N),N=2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions. Address after August 1991: Mathematics Department, University of British Columbia, Vancouver, Canada V6T1Y4     

Spaces with flat symmetry in poincaré gauge theory of gravity

A Taub space is considered in the Poincare gauge theory of gravity. It is shown that the torsion tensor has four nonvanishing components, which can be split into two independent pairs S₀₁ ⁰, S₀₁ ¹, and S₂₃ ⁰, S₂₃ ¹. The analysis of the gravitational field equations leads to the conclusion that in this case only a flat space-time with torsion is possible, and that its metric coefficients and the components of the torsion tensor are described by a wave equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–98, April, 1990.