Showing papers on "Explicit symmetry breaking published in 1981"

Particle Physics and Introduction to Field Theory

Abstract: Introduction to field theory mechanics of a finite system the spin-O field the spin-1/2 field Feynman diagrams quantam electrodynamics solitons particle physics - order-of-magnitude estimations particle physics - symmetry, general discussion U1 symmetry and P,C invariance isotropic spin and G parity SU3 symmetry time reversal CPT invariance K-K system vacuum as the source of asymmetry particle physics - interactions Quark confinement hadrons weak interactions weak and electromagnetic gauge theory Quark-Parton model and high-energy processes chiral symmetry.

Coexistence of Spin-Glass and Ferromagnetic Orderings

Abstract: The phase diagram of the infinite-range model of spin-glasses exhibits two mixed phases. In these mixed phases, ferromagnetism and spin-glass order coexist, due to freezing of the transverse degrees of freedom or replica symmetry breaking. This may help to interpret a number of recent experimental findings, e.g., in $\mathrm{Au}\mathrm{Fe}$.

Symmetry and bifurcations of momentum mappings

Abstract: The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.

On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems

Abstract: We develop a unified approach, based on Araki's relative entropy concept, to proving absence of spontaneous breaking of continuous, internal symmetries and translation invariance in two-dimensional statistical-mechanical systems. More precisely, we show that, under rather general assumptions on the interactions, all equilibrium states of a two-dimensional system have all the symmetries, compact internal and spatial, of the dynamics, except possibly rotation invariance. (Rotation invariance remains unbroken if connected correlations decay more rapidly than the inverse square distance.) We also prove that two-dimensional systems with a non-compact internal symmetry group, like anharmonic crystals, typically do not have Gibbs states.

Spontaneously Generated Gravity

Abstract: We show, following a recent suggestion of Adler, that gravity may arise as a consequence of dynamical symmetry breaking in a scale- and gauge-invariant world. Our calculation is not tied to any specific scheme of dynamical symmetry breaking. A representation for Newton's coupling constant in terms of flat-space quantities is derived. The sign of Newton's coupling constant appears to depend on infrared details of the symmetry-breaking mechanism.

Nonlinear σ model in the loop expansion

Abstract: The nonlinear $\ensuremath{\sigma}$ model in four dimensions is discussed in the context of the loop expansion. Since the model is perturbatively nonrenormalizable, divergences not of the form of the Lagrangian are of course expected; what is perhaps surprising is that there are divergences which appear not to be invariant under the original nonlinear symmetry. We demonstrate, however, that these apparently noninvariant terms do not contribute to on-mass-shell quantities and may be eliminated order by order by a field redefinition involving space-time derivatives. The linear $\ensuremath{\sigma}$ model is then examined in detail; it is shown how the nonlinear model, including the apparently noninvariant terms, emerges as the limit of the linear model as the $\ensuremath{\sigma}$ mass goes to infinity. Finally, we compare our approach with other treatments of the "noninvariant" terms in the nonlinear model.

Renormalizable Theories with Symmetry Breaking

Abstract: The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and an arbitrary field multiplet, the expected integrated Ward identity are shown to hold to all orders of renormalized perturbation theory provided the Lagrangian is suitably chosen. The corresponding local Ward identity which provides the Lagrangian version of current algebra through the coupling to an external classical Yang-Mills field, is then proved to hold up to the classical Adler-Bardeen anomaly whose general form is written down. The BPHZ renormalization scheme is used throughout in such a way that the algebraic structure analyzed in the present context may serve as an introduction to the study of fully quantized gauge theories.

Dynamically broken chiral symmetry with bag confinement

Abstract: We lay the groundwork for a model of low-lying mesons in the spirit of the MIT bag model but which also takes into account dynamical chiral-symmetry breaking. We depart from the static cavity approximation in that we dynamically break chiral symmetry prior to confinement and we confine only in the qq-bar relative coordinate. We show that single-gluon exchange in the qq-bar system is a strong component of the force that drives the symmetry breaking. We verify that our approximations respect the chiral Ward identity prior to confinement. For the pion, we find that our boundary condition on the relative coordinate results in a small chiral breaking in that it raises the pion mass from zero to approx.120 MeV.

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

Abstract: Using the Bogoliubov inequality, we extend previously known results concerning the absence of continuous symmetry breakdown for equilibrium states of certain quantum and classical lattice, and continuum systems in two space dimensions.

Case of broken symmetry in the quadratic Zeeman effect

Abstract: A particularly simple instance of broken symmetry arises in the problem of a hydrogen atom in a uniform magnetic field. In a limited sense, the magnetic Hamiltonian nearly commutes with the unit projection of the Runge-Lenz vector upon the field direction.

Coupling-constant flows and dynamical symmetry breaking

Abstract: The Coleman-Weinberg theory is reformulated in terms of flows in coupling-constant space. It is shown that the existence of dynamical symmetry breaking is essentially governed only by the renormalization-group β functions. An application is made to the massless Weinberg-Salam model.

Space-time topology and spontaneous symmetry breaking

Abstract: Spontaneous symmetry breaking of a gauge theory with topological charge is studied in an arbitrary space-time. Sets of relations on the topological charges are found which, if not satisfied, inhibit the symmetry breaking from that particular sector. Different solutions to these relations correspond to a symmetry breaking into topologically inequivalent gauge sectors of the residual symmetry group.

Symmetry breaking for molecular open systems

Abstract: -We study the modifications to the energy levels of a molecule due to its interaction with an external boson (phonon or photon) reservoir. In the Hartree approximation it is shown that this leads to a non-linear functional, whose stationary states may break the symmetries of the isolated molecular Hamiltonian. These symmetries may often be restored by use of the generator coordinate method, which amounts to dressing the molecule with its boson cloud. The significance of these constructions for recent discussions of molecular structure is discussed. §

Percolation for low energy clusters and discrete symmetry breaking in classical spin systems

Abstract: We consider classical lattice systems in two or more dimensions with general state space and with short-range interactions. It is shown that percolation is a general feature of these systems: If the temperature is sufficiently low, then almost surely with respect to some equilibrium state there is an infinite cluster of spins trying to form a ground state. For systems having several stable sets of symmetry-related ground states we show that at low temperatures spontaneous symmetry breaking occurs because in a two-dimensional subsystem there is a unique infinite cluster of this type.

A Note on the Stability of Phase Diagrams in Lattice Systems

Abstract: We construct a class of non-symmetry breaking pair interactions, which change the phase diagram of then.n. Ising and classicalX Y model. Furthermore we improve earlier obtained constraints on the decrease of interactions, necessary to get analyticity properties of the pressure in manifolds of non-symmetry breaking interactions.