Chiral symmetry breaking at finite temperature in Coulomb gauge QCD

Chiral symmetry breaking at finite temperature is analysed in Coulomb gauge QCD, using a suitably renormalised gap equation. In Coulomb gauge the gap equation is derived using the Ward identities and the Dyson equations for the vector and axial-vector vertices. Making the ladder approximation to the Bethe-Salpeter kernel relates the chiral symmetry breaking parameters to the static quark potential. It is thus possible to use a confining potential in the analysis of chiral symmetry breaking. We extend this to finite temperature. For a confining potential there is no chiral symmetry restoration at any finite temperature.     

Effective lagrangians with U(1) axial anomaly (I)

The effective lagrangian which includes the U(1) axial anomaly is discussed. The lagrangian describes the interaction of physical mesons of spin-zero and spin-one fields and an effective Kogut-Susskind four-vector anomaly field. The interactions are constructed which satisfy all the anomalous Ward identities for vertices which accommodate arbitrary amounts of chiral and SU(3) symmetry breaking consistent with U(3) × U(3) current algebra.     

Mesons in the Quark Model of Superconductivity Type

On the basis of a quark model of superconductivity type, effective chiral Lagrangians are obtained for strong, electromagnetic and weak interactions of scalar, pseudoscalar, vector and axial vector meson nonets at low energies. The spontaneous breaking of chiral symmetry plays an important role. The form factors of strong and electromagnetic vertices, meson masses and different types of meson decaysare discussed.     

Three-dimensional annihilation imaging of trapped antiprotons

We demonstrate three-dimensional imaging of antiprotons in a Penning trap, by reconstructing annihilation vertices from the trajectories of the charged annihilation products. The unique capability of antiparticle imaging has allowed, for the first time, the observation of the spatial distribution of the particle loss in a Penning trap. The radial loss of antiprotons on the trap wall is localized to small spots, strongly breaking the azimuthal symmetry expected for an ideal trap. Our observations have important implications for detection of antihydrogen annihilations.     

Full fermion-boson vertex function derived in terms of symmetry relations in Abelian gauge theory

Nonperturbative studies such as confinement and dynamical chiral symmetry breaking need the nonperturbative interacting vertex functions. In this paper, an approach to determining the full fermion-boson vertex function in four-dimensional Abelian gauge theory is presented: this full vertex function is derived in terms of a set of normal (longitudinal) and transverse Ward-Takahashi relations for the fermion-boson (vector) and axial-vector vertices in the momentum space in the case of massless fermion. Such a derived fermion-boson vertex function should be satisfied both perturbatively and nonperturbatively. The fact that such a derived full fermion-boson vertex function to one-loop order holds indeed is proven and the nonperturbative form of this vertex is also under discussion.     

A model of intrinsic symmetry breaking

Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry.     

Solvent-induced symmetry breaking

Symmetry breaking can be induced in a number of ways including interactions with a solvent. An example is the triiodide ion which is centrosymmetric in the gas phase. Molecular dynamics simulations of the triiodide ion in solution have been used to investigate the extent of symmetry breaking in a variety of solvents. We find that the triiodide ion loses its symmetry in water, ethanol, and methanol which form hydrogen bonds with the ion. This results in a localization of charge at one end of the ion and breaking of the geometric symmetry. The extent of symmetry breaking increases as the temperature is lowered. Correlation times for interconversion are reported and the energetics of symmetry breaking are presented. Analogies are made with second-order phase transitions.     

Effects of symmetry breaking in finite quantum systems

The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

The breaking of quantum double symmetries by defect condensation

In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one originally proposed in F.A. Bais, B.J. Schroers, J.K. Slingerland [Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601]; Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068], and therefore extends the number of possible breaking patterns that can be described consistently. We start by recalling why the extended symmetry notion of quantum double algebras is an optimal tool when analyzing a wide variety of two-dimensional physical systems including quantum fluids, crystals and liquid crystals. The power of this approach stems from the fact that one may characterize both ordinary and topological modes as representations of a single (generally nonabelian) Hopf symmetry. In principle a full classification of defect mediated as well as ordinary symmetry breaking patterns and subsequent confinement phenomena can be given. The formalism applies equally well to systems exhibiting global, local, internal and/or external (i.e. spatial) symmetries. The subtle differences in interpretation for the various situations are pointed out. We show that the Hopf symmetry breaking formalism reproduces the known results for ordinary (electric) condensates, and we derive formulae for defect (magnetic) condensates which also involve the phenomenon of symmetry restoration. These results are applied in two papers which will be published in parallel [C.J.M. Mathy, F.A. Bais, Nematic phases and the breaking of double symmetries, arXiv:cond-mat/0602109, 2006; F.A. Bais, C.J.M. Mathy, Defect mediated melting and the breaking of quantum double symmetries, arXiv:cond-mat/0602101, 2006].     

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.     

Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics

The combined experimental and numerical study finds a complex mechanism of Z(2) symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z(2) symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z(2)-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z(2) symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.     

Symmetry breaking breaks friction

The harmonic analysis of the symmetry breaking is used to study the interaction and inter-layer motion of double-wall carbon nanotubes shells. The tremendous total symmetry reduction with respect to the high symmetry of the isolated layers results in low interaction: its decreasing with the symmetry breaking rate explains the observed small friction.     

Spontaneous breaking of spatial and spin symmetry in spinor condensates

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously formed patterns in the longitudinal magnetization.     

三维量子自旋玻璃理论(Ⅲ)──replica对称破缺解

利用推广的Ｐａｒｉｓｉ量子ｒｅｐｌｉｃａ对称破缺方案，将我们以前提出的理论推广到ｒｅｐｌｉｃａ对称破缺，获得一组新的自旋自作用和自旋玻璃序参数的自洽方程，导出局域磁化率．通过计算ｒｅｐｌｉｃａ对称破缺自由能，发现矢量自旋玻璃模型的ｍｐｌｉｃａ对称解存在着低温破缺． 关键词：     

Low-lying excited states of quantum antiferromagnets on a triangular lattice

We study low-lying states of theXY and Heisenberg antiferromagnets on a triangular lattice to clarify whether spontaneous symmetry breaking occurs atT=0 in the thermodynamic limit. Approximate forms of low-lying states are proposed, in which degrees of freedom of the sublattice magnetization and of the chirality are separated. These approximate states have a long-range order and twofold structures. It is shown that low-lying states can be accurately described with the present approximation. It has been argued that low-lying states play an important role in symmetry breaking. With the help of this approximation, we discuss the contribution of low-lying states to symmetry breaking of two types, namely creation of the spontaneous sublattice magnetization and the spontaneous chirality. Furthermore, to show evidence for the occurrence of symmetry breaking, we numerically study the low-lying states of finite systems of theXY and Heisenberg antiferromagnets. It is found that the necessary conditions for the symmetry breaking to occur are satisfied in these models.     

Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation

By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation.