Nonperturbative Spontaneous Symmetry Breaking

A nonperturbative approach for spontaneous symmetry breaking is proposed. It is based on some conjectural properties of interacting field operators. As the consequences an additional terms like to m ² A ² appears in the initial Lagrangian.     

Exactly Solvable Models and Spontaneous Symmetry Breaking

We study a few two-dimensional models with massless and massive fermions in the hamiltonian framework and in both conventional and light-front (LF) forms of field theory. The new ingredient is a modification of the canonical procedure by taking into account solutions of the operator field equations. After summarizing the main results for the derivative-coupling and the Thirring models, we briefly compare conventional and LF versions of the Federbush model including the massive current bosonization and a Bogoliubov transformation to diagonalize the Hamiltonian. Then we sketch an extension of our hamiltonian approach to the two-dimensional Nambu–Jona-Lasinio model and the Thirring-Wess model. Finally, we discuss the Schwinger model in a covariant gauge. In particular, we point out that the solution due to Lowenstein and Swieca implies the physical vacuum in terms of a coherent state of massive scalar field and suggest a new formulation of the model’s vacuum degeneracy.     

Periodic Square-Well Potential and Spontaneous Breakdown of PT-symmetry

A particle moving on a circle in a purely imaginary one-step potential is studied in both the exact and broken PT-symmetric regime.     

Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.     

Symmetry and Integrability in the Classical Model of Zitterbewegung

We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.     

Spontaneous Electro-Weak Symmetry Breaking and Cold Dark Matter

In the standard model, the weak gauge bosons and fermions obtain mass after spontaneous electro-weak symmetry breaking, which is realized by one fundamental scalar field, namely the Higgs field. We study the simplest scalar cold dark matter model in which the scalar cold dark matter also obtains mass by interaction with the weakdoublet Higgs field, in the same way as those of weak gauge bosons and fermions. Our study shows that the correct cold dark matter relic abundance within 3a uncertainty （0.093 〈 Ωdmh^2 〈 0.129） and experimentally allowed Higgs boson mass （114.4 ≤ mh≤ 208 GeV） constrain the scalar dark matter mass within 48 ≤ ms ≤ 78 GeV. This result is in excellent agreement with the result of de Boer et al. （50 ~ 100 GeV）. Such a kind of dark matter annihilation can account for the observed gamma rays excess （10σ） at EGRET for energies above 1 GeV in comparison with the expectations from conventional Galactic models. We also investigate other phenomenological consequences of this model. For example, the Higgs boson decays dominantly into scalar cold dark matter if its mass lies within 48 ~ 64 GeV.     

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.     

Quantum and Classical Coincidence Imaging in Spontaneous Parametric Down-conversion

Two-photon coincidence imaging (It is also called quantum or ghost imaging) can be carried out by an entangled two-photon quantum state.But a recent experiment (R.S.Bennink, et al, Phys.Rev.Lett.89, (2002) 113601) shows that this effect can be achieved using a classical source with a pair of correlated beams.In this work, we show that quantum and classical coincidence imaging can be incorporated into an optical system by using the spontaneous parametric down-conversion beam.The features of quantum and classical coincidence imaging are discussed.     

Spontaneous Disturbance of Symmetry in Bianchi Types III and VIII Metrics

Russian Physics Journal - Spontaneous disturbance of gauge symmetry in cosmology, including that in cosmological models with rotation, has been investigated in a number of studies. In this work, a...     

A Classical Toda Family with a Common Virasoro Symmetry Algebra

By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.     

On the Hidden Symmetry Algebras of the Classical Principal Chiral Model

The hidden symmetries of the principal chiral model are studied by using the new infinitesimal Riemann-Hilbert transformations. It is found that the algebra of hidden symmetries decomposes into the semidirect sum of the loop algebra and the conformal algebra of the plane, where both subalgebras are Lie multi-algebras with each Lie product being a Baxter-Lie product with respect to some special solution of the modified classical Yang-Baxter equation. Two special examples of the Lie products are given, which are consistent with Wu's, Avan and Bellon's results.     

Relativistic Hydrodynamics of Color-Flavor Locking Phase with Spontaneous Symmetry Breaking

We study the hydrodynamics of color-flavor locking phase of three flavors of light quarks in high density QCD with spontaneous symmetry breaking. The basic hydrodynamic equations are presented based on the Poisson bracket method and the Goldstone phonon and the thermo phonon are compared. The dissipative equations are constructed in the frame of the first-order theory and all the transport coefficients are also defined, which could be looked on as the general case including the Landau's theory and the Eckart's theory.     

Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions

Abstract

We study the general applicability of the Clarkson–Kruskal’s direct method, which is known to be related to symmetry reduction methods, for the similarity solutions of nonlinear evolution equations (NEEs). We give a theorem that will, when satisfied, immediately simplify the reduction procedure or ansatz before performing any explicit reduction expansions. We shall apply the method to both scalar and vector NEEs in either 1+1 or 2+1 dimensions, including in particular, a variable coefficient KdV equation and the 2+1 dimensional Khokhlov–Zabolotskaya equation. Explicit solutions that are beyond the classical Lie symmetry method are obtained, with comparison discussed in this connection.     

A Model with Spontaneous Symmetry Breaking and Its Kink Soliton Solution

A model with spontaneous symmetry breaking is presented. The exact kink which is stable and kink lattice solutions are obtained. When the parameter of the model λ tends to zero, all the results reduce to those of the well-known Φ⁴ model.     

Spontaneous Symmetry Breaking and Higgs' Mechanism in the Nonsymmetric Jordan-Thiry Theory

In the paper we construct the nonsymmetric Jordan-Thiry theory unifying Moffat's theory of gravitation, the Yang-Mills' field, the Higgs' fields and scalar forces in a geometric manner. We discuss spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory. The scalar field Ψ (as in classical Jordan-Thiry theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behavior. We discuss the relation between R₊ invariance and U(1)_F from G. U. T. within Einstein λ-transformation, and fermion number conservation. In this way we connect W _μ-field from nonsymmetric theory of gravitation with a gauge field A from G. U. T. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

The Effect of Spontaneous Breaking of Gauge Symmetry in Cosmology with Rotation

The effect of spontaneous breaking of gauge symmetry is studied for cosmological models with expansion and rotation with the Bianchi metrics of types II, IV, V, and VI. The conditions are defined wherein the effect is manifested in these models.     

Spontaneous U（1） Symmetry Breaking in Coupled Bose System

Adding a U(1) symmetry breaking term V^1/2 a(λ₁a₀+λ*₁a^†₀)+V^1/2(λ₂b₀+λ^*₂b^†₀) to Bogoliubov's truncated Hamiltonian H_B for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we find that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU(1,1) × SU(1,1) coherent states. The Bose-Einsteincondensation occurs in response to the spontaneous U(1) symmetry breaking.