Solitons in models with dynamical spontaneous symmetry breaking

An approximate quasi-classical method for the investigation of solitons appearing at quantum level is described. The existence of the soliton in the model with Yukawa coupling in two-dimensional space-time is established with the help of this method. The existence of solitons in the Georgi-Glashow type model with dynamical spontaneous symmetry breaking is shown.     

Dual models and spontaneous symmetry breaking

The question of spontaneous symmetry breaking in dual models is investigated. In the context of a particular model with a conserved “charge”, two different approaches to the problem, spurion emission and the effective potential methods, are developed. A method is described for the calculation of the effective potential, and it is applied to determine the first few terms of the potential.     

Gravitation and spontaneous symmetry breaking

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature.Research supported by the Arnow Chair in Astrophysics.     

Decoherence induced spontaneous symmetry breaking

We study time dependence of exchange symmetry properties of Bell states when two-qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of 0.5 at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states under local, quantum mechanical noise which is modeled by two identical spin baths. Results turn out to be very similar to the classical case. We identify decoherence as the main mechanism leading to breaking of qubit exchange symmetry.     

Renormalizable models with simple symmetry breaking

If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.     

Spontaneous symmetry breaking in cosmological models with rotation

We study the possibility of spontaneously broken gauge symmetry in the theory of a charged massive or massless scalar field for cosmological models of the Gödel and Ozsvath-Schücking types. We consider the effect of spontaneous symmetry breaking in the construction of a new cosmological solution with rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–26, February, 1989.The author thanks the participants of the seminars of Prof. A. A. Grib and Prof. D. D. Ivanenko for discussions of the results.     

CP nonconservation and spontaneous symmetry breaking

The observed CP violation is assumed to be due to the spontaneous symmetry-breaking mechanism; the Lagrangian is CP invariant but its particular solution is not. The general classification of such theories when coupled with different unified gauge models of the weak and electromagnetic interactions is given. All such theories lead naturally to a basically milliweak CP noninvariant solution. The possibility that for most weak transitions the result may resemble a superweak theory is analysed, and possible experiments to distinguish these two different types of theories are discussed. Detailed calculations for various CP violating amplitudes are carried out for a generalized Georgi-Glashow model.     

Group theory of spontaneous symmetry breaking

The connection between the minimality of the Higgs field potential and the maximal little groups of its representation obtained by spontaneous symmetry breaking is analyzed. It is shown that for several representations the lowest minimum of the potential is related to the maximal little group of those representations. Furthermore, a practical necessity criterion is given for the representation of the Higgs field needed for spontaneous symmetry breaking.     

The geometry of spontaneous symmetry breaking

The problem of classifying the theoretically allowed patterns of spontaneous symmetry breading, in theories where the ground state is determined as a minimum of a G-invariant potential (G a compact group of transformations), is analyzed. A detailed, complete, and rigorous justification of a recently proposed approach to the determination of the minima of G-invariant potentials [10.] is presented. The results are obtained through an analysis of the geometry of the finite-dimensional representations of G, which leads to a complete characterization of the structure of orbit space and its partition in subsets (strata) formed by orbits with the same symmetry under G-transformations (orbit type), and to a new theorem stating that the gradients of complex analytic G-invariant functions annihilate on one-dimensional strata. Polynomial potentials in particular are studied. Conditions for instability of the residual symmetry (second-order phase transitions) are determined.     

Scale invariance and spontaneous symmetry breaking

Spontaneous breaking of gauge symmetries is studied in theories with nonlinearly realized scale invariance. The classically sliding vacuum expectation values are fixed through quantum corrections. The anomaly of the dilatation current determines the vacuum energy density as well as the dilaton mass. The coupling of gravity to matter is modified in such a way that the cosmological constant vanishes.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Gauge symmetry breaking in matrix models

We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way. The mechanism is based on the presence of some extra (matrix) dimensions. These extra dimensions are different from the usual ones which give to a noncommutative geometry of the Grönewold-Moyal type, and are reminiscent of the Connes-Lott model, although the action is very different.     

Radiative symmetry breaking in supersymmetric models

We propose a scheme where the three relevant physics scales related to the supersymmetry, electroweak, and baryon minus lepton (B−L) breakings are linked together and occur at the TeV scale. The phenomenological implications in the Higgs and leptonic sectors are discussed.     

PT symmetry and spontaneous symmetry breaking in a microwave billiard

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.     

Covariance of spontaneous symmetry breaking in non-inertial frames

It is pointed out that contrary to a recent claim the process of symmetry breaking is covariant in a non-inertial frame.     

Dynamical symmetry breaking in models with the Yukawa interaction

The models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction are discussed. The chiral condensate and the fermion mass are calculated analytically through a one-loop approximation in (1 + 1)-dimensions. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.