Unified Gauge Theories Research Articles

A Viable Model of Locally Anisotropic Space-Time and the Finslerian Generalization of the Relativity Theory

The work is devoted to the construction of a viable model of locally anisotropic, i.e. Finslerian, space-time and to the generalization, on this basis, of the relativistic theory of gravitation. Arguments in favour of this model are considered. From physical considerations the concrete form of the Finslerian metric has been reconstructed and within the framework of the correspondence principle a formalism of the theory has been developed. The approach suggested is aimed at developing unified gauge theories of all fundamental interactions. Much attention is given to the nontrivial physical manifestations of local space anisotropy and to the possibility of its experimental detection.

Unified gauge theories in non-commutative geometry

Abstract We generalize the prescription of Connes in non-commutative geometry to construct unified gauge theories in particle physics. The physical space-time is taken to be a product of a riemannian four-manifold by a discrete set of points. The “algebra of functions” is defined over a space of matrices, and three models are constructed. The first one in which the discrete space consists of two points gives the SU (2) × U (1) gauge theory, broken spontaneously to U (1), and corresponds to the standard model. In the second model, the discrete space has three points, two of which are permutation-symmetrical. It is similar to the minimal SU (5) model of Georgi and Glashow, and all the fermions fit into one spinor representation. The third is the left-right symmetric model SU (2)L × SU (2)R × U (1)B−L model, where the discrete space consists of four points, with a permutation symmetry between the first two and the last two.

Baryogenesis from collapsing topological defects

Topological defects in or coupled to grand unified gauge theories can trap a substantial fraction of the energy density of the universe. When the defects collapse, they release energy in the form of superheavy particles. In theories with CP and baryon number violation, this may lead to an enhanced net baryon to entropy ratio. We explicitly study cosmic string loop, texture and global monopole annihilation.

Gauge fields

This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether’s theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (‘‘the gauge principle’’) that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether’s theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification—all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment.

Unified spin gauge theory of electroweak and gravitational interactions

A spin gauge theory describing fundamental fermions and their electroweak and gravitational interactions is proposed. It is modelled on an eight-dimensional curved manifold M and uses its associated Clifford algebra. The elements of the algebra are represented by 16*16 matrices and the fermions are represented by sixteen-component column vectors. The frame field is introduced as a result of factorising the fermion mass term in the Lagrangian density and is included in an extended covariant derivative. The usual gauge theoretic technique of defining free bosonic Lagrangians from the fermion covariant derivative, when applied to the extended covariant derivative, gives the correct mass matrix for the photon, W and Z bosons, together with the Einstein-Hilbert gravitational Lagrangian density modified at short distances by a term quadratic in the curvature coefficients. Transformation of the Lagrangian by an inner automorphism of the Clifford algebra gives the correct mass and interaction terms for the up and down quarks.

A neutrino with a large magnetic moment and a naturally small mass

Abstract We examine the question of having large magnetic moment for the electron neutrino (needed in one proposed solution to the solar neutrino puzzle) while keeping its mass naturally small in unified gauge theories. We present a phenomenologically viable model realizing this idea in an SU(3)L×U(1) extension of the standard model, where one embeds an SU(2) gauge symmetry transforming a neutrino to an antineutrino. The model predicts new physics in the neutral and charged current sector, which are testable in the near future.

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincare gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2+ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2+ and 2− particles of equal mass, as well as a massive pseudoscalar.

Naturally light Higgs doublets in grand unified gauge theories

Abstract A new mechanism (the use of the nonrenormalizable interactions for the suppression of the dangerous interactions of the Higgs triplets with quark) for the explanation of the fine-tuning problem is proposed. In the case of supersymmetric E 5 grand unified theories, which may arise as the low-energy limit of superstring theory, we predict nontrivial relations between Yukawa coupling constants of the low-energy superpotential.

Cosmological effects of superconducting strings

Abstract Superconducting cosmic strings are a plausible consequence of symmetry breaking in grand unified gauge theories. The luminosity in electromagnetic radiation of an oscillating current-carrying loop may substantially exceed the luminosity in gravitational radiation. In the typical case considered, the energy released electromagnetically is 1049 erg s−1, or 1066 erg in toto. Several consequences follow from this, the most interesting of which is the possibility that such loops may heat their surroundings, generating large, dense spherical shells of gas. Galaxies forming on these gravitationally unstable shells at moderate redshift will be seen at the present epoch to lie on bubbles having radii in the range 10–20h−1 Mpc if the initial ratio of luminosity in electromagnetic waves to that in gravitational wavess is > 10−3 for mass/length 1022 g cm−1. The required primordial energy density in magnetic fields is > 3 × 10−9 of the radiation energy density, if the charge carriers are bosons or superheavy fermions. Since these shells fill up space, the galaxies will have a distribution similar to that found in a recent survey of the northern sky. When the current saturates, a loop will emit particles copiously, and may be seen as an X-ray source at z ∼ 10–50. Such loops may also contribute significantly to the hard X-ray and γ-ray backgrounds and to 1020 eV cosmic rays.

Progress and bottlenecks in simulating lattice gauge theory with fermions

We present a progress report in lattice gauge theory computer simulations which includes the effects of light, dynamical fermions. Microcanonical and hybrid microcanonical-Langevin alogrithms are presented and discussed. A method for “accelerating” stochastic differential equations and defeating critical slowing down is reviewed. Physics applications such as the thermodynamics of quantum chromodynamics, hierarchal energy scales in unified gauge theories, and the phase diagram of theories with many fermion species are discussed. Prospects for future research are assessed.

Ontological Economy and Grand Unified Gauge Theories

In his paper, “Grand Unified Gauge Theories and the Number of Elementary Particles,“ Robert Weingard (1984) suggests what he calls the Extended Redhead's Principle (ERP) for elementary particles: “Two particles for which there are conceivable circumstances in which one can be ‘rotated’ or reoriented into the other are the same (species of) particles” (p. 154). The philosophical soundness of such a principle is questionable.

Energy‐Momentum Tensor and Equations of Motion of Glashow‐Salam‐Weinberg‐Theory in Curved Space‐Time

AbstractThe equations of motion of the unified gauge theory of weak and electromagnetic interactions, when minimally coupled to the gravitational field, are given.

Some remarks on the algebra of Eddington'sE numbers

This paper reviews the algebra of Eddington'sE numbers and identifies those points where Eddington anticipated results of current interest. He discovered the Majorana spinors, and was responsible for the standard γ 5 notation as well as the notion of chirality. Furthermore, Eddington defined Clifford algebras in eight and nine dimensions which are now appearing in grand unified gauge and supersymmetric theories. A point which Eddington cleared up, yet is still misunderstood, is that the Dirac algebra corresponds to afive-dimensional base space.

Spherically symmetric monopoles and dyons with spin

Abstract The collective coordinate method of semiclassical quantization is used to show that the dyonic excitations of certain magnetic monopoles found in unified gauge theories may have nonzero spin, even when the classical monopole fields are spherically symmetric. The magnetic monopoles in the SU(5) model which have three and six times the minimum Dirac magnetic charge provide examples of this phenomenon. The usual relation between spin and statistics is verified for the dyons.

New approach to left-right-symmetry breaking in unified gauge theories

We propose a new approach to the left-right-symmetric models of weak interactions where parity-and ${\mathrm{SU}(2)}_{R}$-breaking scales are decoupled from each other. This changes the spectrum of Higgs bosons, which in turn affects the evolution of various gauge coupling constants with energy. This has profound implications for mass hierarchies in partial unification models based on ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(4)}_{C}$ and grand unified SO(10) models. We find several interesting SO(10)-breaking chains with and without an intermediate ${\mathrm{U}(1)}_{R}$ symmetry for which both ${M}_{{W}_{R}^{\ifmmode\pm\else\textpm\fi{}}}$ and ${M}_{{Z}_{R}}$ masses are in the range of 1-20 TeV. We also find a symmetry-breaking pattern for which the ${\mathrm{SU}(4)}_{C}$-breaking scale is in the range of ${10}^{5}$ GeV. These patterns lead to observable $\ensuremath{\Delta}B=2$ as well as other right-handed-current effects at low energies.

Double beta decay and the neutrino mass

The present state of the problem of the double neutrinoless beta decay, 2β(0ν), and related questions is reviewed. Various mechanisms for ΔL = 2 transitions in models with spontaneous violation of lepton number (L) conservation are discussed. From the standpoint of unified gauge theories, a Majorana neutrino mass would be the most probable reason for processes with ΔL = 2 (if they occur). The 2β(0ν) decay is compared with other phenomena which are sensitive to the neutrino mass. It follows from this comparison that the 2β(0ν) decay is essentially the only process which could be detected at the present level of experimental capabilities and which might tell us about the nature of the neutrino mass, if this mass is some tens of electron volts.

New approach to unified gauge theories

A new approach to unified gauge theories, based upon ''generalized Dirac'' equations, is developed. Consideration of the symmetries of such equations is shown to lead to a general framework within which we may construct unified gauge theories of elementary particles. A symmetry-breaking mechanism is given which incorporates general relativity into this framework.

Grand Unified Gauge Theories and the Number of Elementary Particles

Recently, Michael Redhead has argued that the grouping of particles into multiplets by grand unified gauge theories (GUT's) does not, by itself, imply an ontological reduction in the number of elementary particles. While sympathetic to Redhead's argument, in this note I argue that under certain conditions involving Kaluza-Klein theories, GUT's would provide such an ontological reduction.

Unified gauge theory for electromagnetism and gravitation based on twistor bundles

A unified gauge theory of the combined gravitational and electromagnetic fields is obtained by two different procedures using twistors as a starting point for the construction of the appropriate bundles. One of these formalisms is obtained by relaxing the conditions on the structure of a twistor bundle theory previously developed by the authors for the Poincaré group as the structure group. The other formalism is based on a tensor product bundle and can be readily extended to include structure groups involving direct products of nonabelian groups with the Poincaré group. The results of the theory are compared with those obtained in projective theories of the generalized Jordan–Kaluza–Klein type, and some of the essential differences are pointed out.

Thermodynamic potential of grand unified gauge theories

The thermodynamic potential for an arbitrary asymptotically free unified gauge theory is considered at higher temperatures. The calculations are performed up to O(g4 ln g). The results are further specialised in an SU(5) model and within this model the equation of state is derived for the matter in the very early universe.