Gauge Field Theories on Clifford Algebras

We present a straightforward model of the U(1) gauge equations of Dirac and Maxwell, as well as the U(n) Yang–Mills equations where all fields and gauge transformations take values in a Clifford algebra. When expressed in terms of the Clifford components of the fields, the equations display various gauge symmetries which we intestigate for all Clifford algebras. In particular, for the Pauli algebra, the Dirace CA equations possess the SU(2) × U(1)-symmetry.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

Bäcklund transformations for static axially-symmetric self-dual SU(N) gauge fields

Bäcklund transformations are derived for static axially-symmetric self-dual SU(N) gauge fields. In the case of SU(3) broken to U(1) × U(1), they produce field configurations with fractional topological charges.     

Use of some fermion field identities for bosonisation of U(n) thirring and Schwinger models

A set of identities involving triple products of free fermion fields belonging to the fundamental representation of U(n) is established. These would give a direct bosonised form of U(n) massless as well as massive Thirring model for \(g_\upsilon = - \frac{{4\pi }}{{n + 1}}\) . The identities are also shown to exist for fields whose leading operator product expansion is same as that of free fermion fields. This would then give us an exactly solvable bosonised form of U(n) Schwinger model.     

Effective lagrangians with U(1) axial anomaly (I)

The effective lagrangian which includes the U(1) axial anomaly is discussed. The lagrangian describes the interaction of physical mesons of spin-zero and spin-one fields and an effective Kogut-Susskind four-vector anomaly field. The interactions are constructed which satisfy all the anomalous Ward identities for vertices which accommodate arbitrary amounts of chiral and SU(3) symmetry breaking consistent with U(3) × U(3) current algebra.     

Monte Carlo study of the 3-dimensional abelian Higgs model with radially variable Higgs field

The three-dimensional U(1)-Higgs model with a radially variable Higgs field is studied using a Monte Carlo method. The Higgs fields and the U(1) gauge field variables are considered in the same (fundamental) representation. For various small values of the scalar field self-coupling parameter λ, phase transitions (likely first order) between two completely distinct phases of the theory, are observed.     

Unified geometry of antisymmetric tensor gauge fields and gravity

Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ω_r?1M,U(1)), the U(1) bundles over the space of all (r?1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω₁M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.     

Analog of Electroweak model for contracted gauge group

The limiting case of the bosonic part of the standard Electroweak Model, which corresponds to the contracted gauge group SU(@#@ 2; j) × U(1) is discussed. The Higgs-boson, Z-boson, and electromagnetic fields become external ones with respect to the W-boson fields. The W-boson fields do not affect these external fields. The masses of all particles of the Electroweak Model remain the same under contraction.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

Baryogenesis and entropy generation in a superstring model

We work out details of a previously proposed senario for baryogenesis in a superstring model, based on the Affleck-Dine mechanism exploiting the decays of large expectation values for squark and slepton fields after inflation. We show how the coefficients of the relevant quartic scalar operators can aquire the necessary imaginary parts. We examine possible sources of entropy among the gauge-singlet scalar and fermion fields including the gravitino, as well as the low-energy SU(2)_L × U(1)² → SU(2)_L × U(1)_Y → U(1)_em phase transitions. We argue that none of these dilute substantailly the baryon-to-entropy ratio, which can easily be in the range preferred by cosmology. This means, in particular, that the Polonyi and gravitino problems are solved.     

Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

Compensation and nonlinear theory

The existence is demonstrated of a new class of compensating fields in addition to the well-known fields of Yang-Mills type that lead to nonlinear field theory and induce a non-Euclidean geometry of spacetime. The cases of the Lorentz group, U(1), SU(2), SU(3), SU(2, 2) and coordinate transformations are considered.     

The phase structure of SU(2) × U(1)Y lattice gauge theory

Using analytic and Monte Carlo techniques, we determine the phase structure and nature of spontaneous symmetry breaking of the SU(2) × U(1)_Y electroweak gauge theory with fixed-length Higgs fields on a lattice. We find that it has two completely separated phases: (a) a disordered, symmetric phase and (b) a phase in which SU(2) × U(1)_Y is spontaneously broken to U(1)_em, which is realized in its deconfined Coulomb phase with massless photons. Exact analytic results and approximate series expansions are given for various special cases of the theory.     

Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

q-Deformation of the Krichever–Novikov Algebra

Using q-operator product expansions between U(1) current fields and the corresponding energy-momentum tensors, we furnish the q-analogues of the generalized Heisenberg algebra and the Krichever–Novikov algebra.     

Cylindrically and spherically symmetric monopoles in SU(3) gauge theory

We apply to the Atiyah-Ward ansätze a systematic procedure locating symmetric monopoles in SU(3) gauge theory broken to U(1) × U(1). In particular we recover the known spherically symmetric monopole as a limit of a cylindrically symmetric separated two monopole solution in SU(3). We also discuss the spherically symmetric monopole in SU(n). This latter is the only instance where we have properly shown the smoothness of the Higgs and gauge fields.     

Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

LEFT-RIGHT SYMMETRY MODEL IN WESS-ZUMINO-WITTEN EFFECTIVE ACTION

In the present paper we obtain the Wess-Zumino-Witten effective action of the Goldstone bosons coupling to electroweak fields within the left-right symmetry SU(2)_L×SU(2)_R×U(1) gauge theory with six quarks.     

Analytic results for SU(2)×U(1)Y lattice gauge theory with variable-length Higgs fields

We present analytic results for the electroweak SU(2)×U(1)_Y lattice gauge theory with variable-length Higgs fields and discuss their implications for the phase structure of this theory.