Spontaneous symmetry breaking in a time-dependent space-time

Spontaneous symmetry breaking of a ⁴ quantum of field theory in a time-dependent space-time, de Sitter space, is discussed in the Schrödinger picture. Instead of the usual cutoff method we use an-regularization procedure to deal with the divergent integrals.     

Spontaneous breaking of electric-magnetic charge symmetry in local quantum field theory

It is shown that in local quantum field theory with electric and magnetic currents, duality transformations are always spontaneously broken. Possible implications are discussed leading to the screening of magnetic charge and the failure of the cluster property as in two-dimensional quantum electrodynamics.     

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.     

f-symbols in Robertson-Walker space-time

In a Robertson-Walker space-time, a spinning particle model is investigated. It is shown that in a stationary case a class of new structures called f-symbols exists ￠ Central European Science Journals. All rights reserved.     

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.     

Spontaneous symmetry breaking of arbitrage

We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered by a control parameter. We estimate the control parameter for a momentum strategy with real historical data. The momentum strategy aided by symmetry breaking shows stronger performance and has a better risk measure than the naive momentum strategy in U.S. and South Korean markets.     

Spontaneous symmetry breaking and response functions

We study the quantum phase transition occurring in an infinite homogeneous system of spin 1/2 fermions in a non-relativistic context. As an example we consider neutrons interacting through a simple spin-spin Heisenberg force. The two critical values of the coupling strength—signaling the onset into the system of a finite magnetization and of the total magnetization, respectively—are found and their dependence upon the range of the interaction is explored. The spin response function of the system in the region where the spin-rotational symmetry is spontaneously broken is also studied. For a ferromagnetic interaction the spin response along the direction of the spontaneous magnetization occurs in the particle-hole continuum and displays, for not too large momentum transfers, two distinct peaks. The response along the direction orthogonal to the spontaneous magnetization displays instead, beyond a softened and depleted particle-hole continuum, a collective mode to be identified with a Goldstone boson of type II. Notably, the random phase approximation on a Hartree-Fock basis accounts for it, in particular for its quadratic—close to the origin—dispersion relation. It is shown that the Goldstone boson contributes to the saturation of the energy-weighted sum rule for ≈25% when the system becomes fully magnetized (that is in correspondence of the upper critical value of the interaction strength) and continues to grow as the interaction strength increases.     

Spontaneous symmetry breaking for zero mass

We investigate spontaneous symmetry breaking of a zero mass free Lagrangian within a functional formalism. We find that the boundary conditions of field solutions are responsible for the spontaneous symmetry breaking and this can be incorporated naturally in a functional method.     

Spontaneous symmetry breaking in Reggeon field theory

We consider a Reggeon field theory when the bare or input Regge intercept α_O is greater than one. This corresponds to a negative mass squared term in conventional field theory and allows for a spontaneous symmetry break-down. A theory with Regge intercept at one emerges, restoring the Froissart bound by t-channel considerations alone. In our elementary example the resulting bare trajectory is nearly of the square root variety familiar from s-channel eikonalization of models which violate the Froissart bound.     

Spontaneous breaking of chiral symmetry in QCD

The consistency of iso-spin (SU(3)) symmetry of the vacuum with the spontaneous breakdown of chiral symmetry without the appearance of a U(1) Goldstone boson, is investigated.     

Duffin-Kemmer-Petiau equation in Robertson-Walker space-time

The (1+1)-dimensional Duffin-Kemmer-Petiau (DKP) equation (for spin 0 and 1) in the Robertson-Walker Space-time is solved. The exact solution is then determined for both cases. As an application, the rate of the created particles in the presence of gravity is calculated via the Bogoliubov transformations technique.     

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.     

Spontaneous symmetry breaking in an electromagnetic field-insulator system

Conditions for spontaneous symmetry breaking and generation of quasi-particles in an insulator through which an electromagnetic field propagates are considered. The order parameter of the system is determined. The mass spectrum of the quasi-particles is found in the cases of linear and nonlinear propagation through the medium with and without interfaces.     

Spontaneous symmetry breaking due to polarization corrections

A model of self-interacting scalar and gravitational fields is constructed, in which the vacuum state with spontaneously broken symmetry arises as a solution of the field equations. The gravitational Lagrangian containing curvature-squared contributions is treated in the first-order formalism. The problems of cosmological singularities and conformal anomalies are discussed. In the case of vanishing Weyl tensor and constant scalar curvature, the curvature-squared contributions may be interpreted as being generated by the vacuum polarization, also in first-order formalism.     

Spontaneous symmetry breaking of optimum fluctuations in semiconductors

The optimum fluctuation method (OFM) has been applied to the tails of the density of states, arising near the edges of the spherically symmetric degenerate bands. In this case the optimum fluctuations (OF) have been shown to undergo a qualitative change, as compared to the case of nondegenerate bands, they lose the spherical symmetry and become elongated or flattened. This means that spontaneous breaking of symmetry takes place. In addition to the usual mechanism of tailing due to the potential of impurities, another mechanism connected with the field of random deformations, arising due to difference in the size of the guest and host atoms, has been also considered. The method used for treating this problem is intimately related to the techniques of the theory of self-trapping. The density of states in the tails, and in some cases the shape of OFs, have been found for all the cases under consideration.