Spatial symmetry breaking and coexistence of attractors in a nonlinear ring cavity

We consider a passive optical system consisting of a ring cavity and a homogeneously broadened two-level medium. We find that a spatial modulation of the input beam imposes processes of competition between the external modulation frequency and the internal space frequencies which emerge from modulation instabilities. This leads to symmetry breaking phenomena when both the amplitude and the wavelength of the modulation are increased and results in the coexistence of periodic attractors. We numerically analyze the corresponding bifurcations and find that they can be explained by a generalization of the concept of cooperative frequency locking although the bifurcating attractors are periodic and are not related to linear resonator modes.     

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.     

Electroweak symmetry breaking with hierarchical feature

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Our study is made in those models in which preons are confined by hypercolor gauge interactions to form massless quarks and leptons as well as heavy hyperhadrons or postons. The hierarchical nature of the breaking can be understood by assuming the necessity of infinite-range color interactions in addition to short-range postonic ones. Self-consistent mass equations forN families of quarks are given in an ideal limit in which left-right asymmetric effects and quark-lepton couplings are neglected.     

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.     

Chiral symmetry breaking in QCD

By applying bifurcation theory to a truncated Dyson-Schwinger equation for the quark propagator in massless QCD, we show that dynamical symmetry breaking occurs at a certain critical value of the coupling constant. Essential ingredients are (a) an effective dynamical mass for the gluon, and (b) a running coupling constant.     

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.     

Chiral symmetry breaking in SQCD

Using a spectral function sum rules approach, we derive some constraints among the Goldstone parameters, the lowest dimension vacuum condensates and the mass of the chiral matter superfield in supersymmetric QCD (SQCD). These relations are consistent with previous results on SQCD and complement them.     

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.     

Vacuum instabilities in models with spontaneous symmetry breaking

Adopting as a reference a simple model with spontaneously broken symmetry we show that the extra massless field present in the three approximation in addition to the true Goldstone bosons may induce, through the radiative corrections to its vacuum expectation value, infrared effects which are not compensable without spoiling the symmetry itself. We further extend the analysis to generic lagrangian field models with spontaneous symmetry breaking and prove that the only constraint to their renormalizability arises from the radiative corrections to the vacuum expectation value of the massless fields, except for the true Goldstone bosons which never induce such pathologies.     

Flavor symmetry breaking in DTU

The implications of the breaking of SU (N) flavor symmetry are studied at the planar and cylinder levels of the Dual Topological Unitarization scheme. It is shown that the ρ intercept is constrained to lie between 0.51 and 0.54, and that SU (4) symmetry is necessarily more strongly broken that SU (3). The matrix structure of the cylinder bootstrap equations is shown to suppress many of the problems of the “cylinder extinction of the planar poles”, and to lead to a sensible singularity spectrum.     

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.     

Salam-Weinberg symmetry breaking with superheavy Higgs particles

We discuss here the possibility of the breaking of Salam-Weinberg symmetry by Higgs particles which are superheavy. The symmetry breaking is associated with a nonzero vacuum expectation value of fermion condensates. This mechanism, if operative in nature, will imply the absence of Higgs particles at the weak scale.     

Chiral symmetry breaking in dense matter

The quark condensate in nuclear matter is studied. We relate it to the nuclear sigma commutator, and then treat it as sigma commutator for quasi- particles in a self-consistent way. We find that the deviation from the linear expression is large at high density. Received: 20 November 1997 / Revised version: 24 February 1998 / Published online: 16 September 1998     

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.     

Flavour symmetry breaking in antiquark distributions

We show that knowledge of the valence quark distribution of a proton at one value of q², enables one to calculate a contribution to the difference between the distribution of anti-up quarks $\text{(}\text{u}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ and anti-down quarks $\text{(}\text{d}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ in the sea of the proton at higher values of q². This difference can be expressed as a linear combination of the structure functions F₁, for νp → νX and e^?p → e^?p (for which one knows the q² behaviour of the moments) and for $\text{ν}\text{p}\text{→ μ}{}^{\mathrm{?}}\text{X}\text{and}\text{ν}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{X}$ (for which one knows the q² behaviour of the odd moments). The calculable contribution involves a non-trivial continuation of the even (odd) moments of the neutral (charged) current structure functions to odd (even) moments. We calculate this contribution and although we find that its sign is negative we point out that this cannot be interpreted as a consequences of the Pauli exclusion principle. We discuss the constraints our results impose on antiquark distributions.