Integrable Deformations of Heisenberg Supermagnetic Model

We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.     

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)×U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ^± and Z ⁰ bosons fields and the Higgs scalar fields.     

Gauge Formulation for Two Potential Theory of Dyons

Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from the symmetry of duality and gauge invariance. Accordingly, the manifestly covariant, dual symmetric and gauge invariant two potential theory of generalized electromagnetic fields of dyons has been developed consistently from U(1)×U(1) gauge symmetry. Corresponding field equations and equation of motion are derived from Lagrangian formulation adopted for U(1)×U(1) gauge symmetry for the justification of two four potentials of dyons.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).     

Incompatibility of New Symmetry Reductions in U(1) × U(2) × U(3) Gauge Group with Higgs Mechanism

Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on U(3) × U(2) × U(1) can be transcribed to NC space-time consistently with these constraints (Chaichian et al., Eur. Phys. J. C29:413, 1). In fact, through two new symmetry reduction mechanisms, this gauge group is reduced to the usual standard model one. In this paper, we show that, on the contrary to the usual standard model, the Goldestone boson equivalence theorem is violated due to the incompatibility of the new symmetry reduction mechanisms with the electroweak Higgs mechanism.

     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

Toward a universal Lagrangian

A gauge theory with the gauge groupU(1)×U(1)×SU(2)×SU(3)×SU(4) is shown to fit well into the generalized Kaluza scheme with eleven-dimensional space-time and its compact subspaceS ²×S ⁵. A unified theory is obtained which exhibits some broken super-symmetric features (N = 8). Our approach is dictated by phenomenological requirements. The appearance of three generations of leptons and six flavors of colored quarks follows naturally. Within our Lagrangian there appear several free parameters (coupling constants), but some relations between them may follow from the requirement of cancellation of divergencies.Temporarily at Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Rd., Dublin 4, Ireland.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

New physics contribution to neutral trilinear gauge boson couplings

We study the one-loop new physics effects to the CP even triple neutral gauge boson vertices γ ^⋆ γ Z, γ ^⋆ Z Z, Z ^⋆ Z γ and Z ^⋆ ZZ in the context of Little Higgs models. We compute the contribution of the additional fermions in Little Higgs models in the framework of direct product groups where [SU(2)×U(1)]² gauge symmetry is embedded in SU(5) global symmetry and also in the framework of the simple group where SU(N)×U(1) gauge symmetry breaks down to SU(2) _L ×U(1). We calculate the contribution of the fermions to these couplings when T parity is invoked. In addition, we re-examine the MSSM contribution at the chosen point of SPS1a′ and compare with the SM and Little Higgs models.     

Fermion masses generated by radiative corrections in aSU(2) L ×SU(2) R ×U(1) B-L model

A new model based on aSU(2) ^R ×SU(2) ^L ×U(1) ^B-L gauge symmetry group is presented. Fermion masses are generated by radiative corrections.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S² (already described in a previous paper) and the SU (3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.     

The Unified SU(2) × U(1) × U′(1)-models of Electroweak Interaction of Leptons

The possible variants of the unified models of electroweak interaction of leptons in the framework of the broken gauge SU(2) × U(1) × U′(1)-symmetry are constructed. In the first part analysis of SU(2) × U(1) × U′(1)-symmetry breaking by the different combinations of two types of Goldstone-Higgs fields: isodoublet φ and isosinglet Φ complex isovector ξ and Φ φ and ξ is considered. The second part is devoted to the construction of the feasible leptonic models in which the masses of the introduced leptons can be generated by symmetry breaking due to the fields considered in the first part. In the third part acceptability of these models from the point of view of available experimental data of cross-sections of muonic neutrino and antineutrino scattering on electron has been investigated.     

Ternary Z2 × Z3 Graded Algebras and Ternary Dirac Equation

The wave equation generalizing the Dirac operator to the Z₃-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors, and is therefore invariant under the product group Z₂ × Z₂ × Z₃. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) × U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.

     

Phase portrait ofSU(5) model. II intermediate phasesSU(3)×[U(1)]2 and [SU(2)]2×[U(1)]2

The effective potential of the scalar field in theSU(5) model has extrema with symmetry:SU(5),SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]², [SU(2)]²×[U(1)]². In our recent paper it was shown that theSU(4)×U(1) phase as well asSU(3)×SU(2)×U(1) phase were stable at the nonzero temperature in a vast region of parameters. In the present paper it is found that the [SU(2)]²×[U(1)]² symmetric vacuum is unstable and theSU(3)×[U(1)]² symmetric vacuum can be metastable in the certain interval of the temperature. Domains of the three phases:SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]²-could co-exist in the early. Universe.     

Phenomenology ofSO(10) unified superstring models with intermediate scaleSU R(2) breaking

Electroweak breaking and the supersymmetric particle spectrum are discussed in superstring theories where the gauge group after compactification isSO(10)×E _s ^′ , and where the gauge symmetry after flux breaking isSU(3)×SU(2)×SU(2)×U(1).     

Stability of proton and maximally symmetric minimal unification model for basic forces and building blocks of matter

With the hypothesis that all independent degrees of freedom of basic building blocks should be treated equally on the same footing and correlated by a possible maximal symmetry, we arrive at a 4-dimensional space-time unification model. In this model the basic building blocks are Majorana fermions in the spinor repre- sentation of 14-dimensional quantum space-time with a gauge symmetry GM4D = SO(1,3)×SU(32)×U(1)A×SU(3)F. The model leads to new physics including mirror particles of the standard model. It enables us to issue some fundamental questions that include: why our living space-time is 4-dimensional, why parity is not con- served in our world, how the stability of proton is, what the origin of CP violation is and what the dark matter can be.     

Supersymmetric anyon model coupled to the electromagnetic field

We construct a supersymmetric gauge model describing the electromagnetic interaction of anyons. This is done by means of the supersymmetric generalization of theU(1) ×U(1) gauge theory. The model contains the statisticalU(1) gauge field endowed with a Chern-Simons mass term and the electromagnetic field, both with the corresponding superpartners, coupled to matter fields. This constrained system is analyzed from the Hamiltonian point of view and the canonical quantization is found. The path-integral method is used to develop the perturbative formalism. We define suitable propagators and vertices and give the diagrammatics and the Feynman rules.     

Twin-unified <Emphasis Type="Italic">SU</Emphasis>(5) × <Emphasis Type="Italic">SU</Emphasis>(5)′ GUT and phenomenology

In this article, after a short introduction, grand unified SU(5)×SU(5)^′ model augmented by D₂ parity has been discussed. The latter turns out to be important for phenomenology. Specific pattern of the GUT symmetry breaking causes new strong dynamics at low energies. Consequently, the Standard Model leptons, along with right-handed /sterile neutrinos, come out as composite states. Issues of the gauge coupling unification, generation of the charged fermion and neutrino masses will be presented. Also, various phenomenological implications and constraints will be discussed.     

QCD bound state calculation of Dalitz decay form factors

We present calculations of the cross-sections and the forward-backward asymmetry forp \(\bar p\) →?⁺ ?^? +X in the framework of anSU(2)×U(1)×G model with two neutral gauge bosons [G=U(1) orSU(2)]. It is shown that a peak in the cross-section associated with a large asymmetry will characterize a deviation from the standard model.