Showing papers on "Explicit symmetry breaking published in 2004"

Decomposition of the elastic tensor and geophysical applications

Abstract: SUMMARY Elasticity is described in general by a fourth-order tensor with 21 independent coefficients, which corresponds to the triclinic symmetry class. However seismological observations are usually explained with a higher order of symmetry using fewer parameters. We propose an analytical method to decompose the elastic tensor into a sum of orthogonal tensors belonging to the different symmetry classes. The method relies on a vectorial description of the elastic tensor. Any symmetry class constitutes a subspace of a class of lower symmetry and an orthogonal projection on this subspace removes the lower symmetry part. Orthogonal projectors on each higher symmetry class are given explicitly. In addition, the method provides optimal higher symmetry approximations, which allow us to decrease the number of independent parameters. Consequences of the symmetry approximation of the elastic tensor on shear wave splitting (SWS) are investigated for upper-mantle minerals (olivine and enstatite), natural samples and numerically deformed olivine aggregates. The orthorhombic part of the elastic tensor as well as the presence of enstatite are important second-order effects.

Minimal supersymmetric grand unified theory: Symmetry breaking and the particle spectrum

Abstract: We discuss in detail the symmetry breaking and related issues in the minimal renormalizable supersymmetric grand unified theory. We find all the possible patterns of symmetry breaking, compute the associated particle spectrum and study its impact on the physical scales of the theory. In particular, the complete mass matrices of the $\mathrm{SU}(2)$ doublets and the color triplets are computed in connection with the doublet-triplet splitting and the $d=5$ proton decay. We explicitly construct the two light Higgs doublets as a function of the Higgs superpotential parameters. This provides a framework for the analysis of phenomenological implications of the theory, to be carried out in a second paper.

Curie's Principle and spontaneous symmetry breaking

Abstract: In 1894 Pierre Curie announced what has come to be known as Curie's Principle: the asymmetry of effects must be found in their causes. In the same publication Curie discussed a key feature of what later came to be known as spontaneous symmetry breaking: the phenomena generally do not exhibit the symmetries of the laws that govern them. Philosophers have long been interested in the meaning and status of Curie's Principle. Only comparatively recently have they begun to delve into the mysteries of spontaneous symmetry breaking. The present paper aims to advance the discussion of both of these twin topics by tracing their interaction in classical physics, ordinary quantum mechanics and quantum field theory. The features of spontaneous symmetry that are peculiar to quantum field theory have received scant attention in the philosophical literature. These features are highlighted here, along with an explanation of why Curie's Principle, though valid in quantum field theory, is nearly vacuous in that context.

Fundamentals of Molecular Symmetry

Abstract: Winner of a 2005 CHOICE Outstanding Academic Book Award Molecular symmetry is an easily applied tool for understanding and predicting many of the properties of molecules. Traditionally, students are taught this subject using point groups derived from the equilibrium geometry of the molecule. Fundamentals of Molecular Symmetry shows how to set up symmetry groups for molecules using the more general idea of energy invariance. It is no more difficult than using molecular geometry and one obtains molecular symmetry groups. The book provides an introductory description of molecular spectroscopy and quantum mechanics as the foundation for understanding how molecular symmetry is defined and used. The approach taken gives a balanced account of using both point groups and molecular symmetry groups. Usually the point group is only useful for isolated, nonrotating molecules, executing small amplitude vibrations, with no tunneling, in isolated electronic states. However, for the chemical physicist or physical chemist who wishes to go beyond these limitations, the molecular symmetry group is almost always required.

Renormalization Group Flows into Phases with Broken Symmetry

Abstract: We describe a method to continue the fermionic renormalization group flow into phases with broken global symmetry. This method does not require a Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally small symmetry-breaking component is inserted into the initial action, as an initial condition for the flow of the self-energy. Its flow is driven by the interaction, and at low scales it saturates at a nonzero value if there is a tendency for spontaneous symmetry breaking in the corresponding channel. For the reduced BCS model, we show how a small initial gap amplitude flows to the value given by the exact solution of the model. We also discuss the emergence of the Goldstone boson in this approach.

Four-Fermion Interaction Model in a Constant Magnetic Field at Finite Temperature and Chemical Potential

Abstract: We investigate an influence of an external magnetic field on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential. By using the Fock-Schwinger proper-time method, we calculate the effective potential for the four-fermion interaction model at the leading order of the $1/N_c$ expansion. A phase structure of the chiral symmetry breaking is shown on $T$-$\mu$, $H$-$T$ and $\mu$-$H$ planes. The external magnetic field modifies the phase structure. It is found that a new phase appears for a large chemical potential.

SO(10) symmetry breaking and type II seesaw formula

Abstract: A minimal SO(10) model with 126 Higgs field breaking B-L symmetry has been shown recently to predict large solar and atmospheric mixings in agreement with observations if it is assumed that the neutrino mass follows from the triplet dominated type-II seesaw formula. No additional symmetries need to be assumed for this purpose. We discuss the conditions on the way SO(10) symmetry breaks down to the minimal supersymmetric standard model (MSSM) and the Higgs multiplets in the model, required for the triplet dominated type-II seesaw formula to hold. We find that (i) SO(10) must break to a nonminimal SU(5) before breaking to the standard model; (ii) B-L symmetry must break at the time of SO(10) breaking and (iii) constraints of unification seem to require that the minimal model must have a 54 dimensional Higgs field together with a 210 and 126 to break the grand unified theory (GUT) symmetry.

Electroweak symmetry breaking in supersymmetric gauge-Higgs unification models

Abstract: We examine the Higgs mass parameters and electroweak symmetry breaking in supersymmetric orbifold field theories in which the 4-dimensional Higgs fields originate from higher-dimensional gauge supermultiplets. It is noted that such gauge-Higgs unification leads to a specific boundary condition on the Higgs mass parameters at the compactification scale, which is independent of the details of supersymmetry breaking mechanism. With this boundary condition, phenomenologically viable parameter space of the model is severely constrained by the condition of electroweak symmetry breaking for supersymmetry breaking scenarios which can be realized naturally in orbifold field theories. For instance, if it is assumed that the 4-dimensional effective theory is the minimal supersymmetric standard model with supersymmetry breaking parameters induced mainly by the Scherk-Schwarz mechanism, a correct electroweak symmetry breaking can not be achieved for reasonable range of parameters of the model, even when one includes additional contributions to the Higgs mass parameters from the auxiliary component of 4-dimensional conformal compensator. However if there exists a supersymmetry breaking mediated by brane superfield, sizable portion of the parameter space can give a correct electroweak symmetry breaking.

Interior symmetry and local bifurcation in coupled cell networks

Abstract: A coupled cell system is a network of dynamical systems, or ‘cells’, coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells and edges that preserves all internal dynamics and all couplings. It is well known that symmetry can lead to patterns of synchronized cells, rotating waves, multirhythms, and synchronized chaos. Recently, the introduction of a less stringent form of symmetry, the ‘symmetry groupoid’, has shown that global group-theoretic symmetry is not the only mechanism that can create such states in a coupled cell system. The symmetry groupoid consists of structure-preserving bijections between certain subsets of the cell network, the input sets. Here, we introduce a concept intermediate between the groupoid symmetries and the global group symmetries of a network: ‘interior symmetry’. This concept is closely related to the groupoid stru...

The symplictic vacuum, exotic quasi particles and gravitational instanton

Abstract: Various experimental studies conducted in the eighties indicated the existence of certain anomalous positron production which could not be accounted for within the generally accepted framework of the standard model. Subsequently several theories were advanced by different investigators notably in Darmstadt, Frankfurt and Cairo to explain the new phenomenon and a neutral meson with a mass equal to 1.8 MeV was predicted by a German group around Greiner and his associates. Concurrently to this development, and seemingly independent of it, some fundamental work by `t Hooft in Utrecht and subsequent studies by Peccei and Quinn in Stanford led Weinberg in Austin to postulate the existence of a new particle which was christened by Wilczek and him the axion. We note that the connection between the Darmstadt–Frankfurt–Cairo–Bristol neutral boson and the axion was not immediately recognized although even a fleeting glance would have revealed the similarity, particularly because the neutral boson was estimated to have a mass of about m =1.8 MeV while the mass of the axion was also conjectured to be m a =1.8 MeV. The present work draws attention to the possibility of relating the said anomalous positron production to certain types of topological defects in the so-called symplictic vacuum of E Infinity theory. These defects, which could be interpreted physically as exotic quasi particles or mini black holes pair production, are created via the instanton mechanism rather than the usual classical gravitational collapse. In turn these “mini” black holes and or exotic particles are perceived experimentally, as an increased rate in the positron production which is not entirely surprising when we note that electrons may be modelled using some forms of mini black hole. The same processes may be seen in a different way as a continuous symmetry breaking of the symmetry on average of the ramified hyperbolic “tiling” geometry of the VAK of the E Infinity vacuum. That means the vacuum fluctuation is the “mechanism” of the symmetry breaking of the VAK. Since symmetry breaking is always accompanied physically by the appearance of a new particle, this VAK fluctuation produces a large family of such symmetry breaking particles of which the axion of the P–Q symmetry breaking is but one of many others. In this manner, the excess production in positrons may be attributed to the disintegration of particles such as the axion which in turn are a consequence of the continuous disintegration and reformation of the symplictic E Infinity VAK via the continuous symmetry breaking vacuum fluctuation. Of course, it is a well-known fact that in the classical limit the rate of production of the aforementioned black holes equals that of ordinary quantum field theory in the sense of Schwinger. However, from a number theoretical view point, E Infinity theory is effectively an extension of quantum field theory into the irrational domain and prior to such limit there is the possibility of a considerably large black hole pair production which could be observed and may be interpreted as anomalous positron production in an experiment using a stack of nuclear emulsions exposed for instance to a beam of 12 C or 22 Ne ions as done by El-Nadi et al. at Cairo University rather than using modern electronic detectors joined to a huge heavy ion accelerator. The paper concludes with observing that the complex symplictic modular group could be used to unify quantum mechanics and general relativity.

Spontaneous symmetry breaking in a non-conserving two-species driven model

Abstract: A two-species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behaviour which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within the mean-field approximation, and compared with Monte Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to be zero, an exact solution is obtained. We present and analyse a physical picture which serves to explain the different phases of the model.

Field Theoretic Realizations for Cubic Supersymmetry

Abstract: We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincare algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems. We investigate some field theoretical aspects of this new symmetry and construct invariant actions for noninteracting fermion and noninteracting boson multiplets. In the case of the bosonic multiplet, where two-form fields appear naturally, we find that this symmetry is compatible with a local U(1) gauge symmetry, only when the latter is gauge fixed by a 't Hooft–Feynman term.

Renormalization group and decoupling in curved space. 3. The Case of spontaneous symmetry breaking

Abstract: We continue investigation of the renormalization group and decoupling of the quantized massive fields in curved space [1]. In the present work we analyze the vacuum sector of a theory, where fields gain their masses due to the Spontaneous Symmetry Breaking (SSB), the case providing the remarkable exception from the Appelquist-Carazzone (AC) theorem in the matter fields sector. Due to the non-minimal coupling between the scalar field and gravity, the vacuum expectation value (VEV) of the scalar is not constant and the induced gravitational action includes an infinite number of non-local terms. Despite this property the theory is renormalizable and the low-energy decoupling in the higher-derivative gravitational sector performs similar to the AC theorem.

Planck-scale effects on global symmetries: Cosmology of pseudo-Goldstone bosons

Abstract: We consider a model with a small explicit breaking of a global symmetry, as suggested by gravitational arguments. Our model has one scalar field transforming under a nonanomalous U(1) symmetry, and coupled to matter and to gauge bosons. The spontaneous breaking of the explicitly broken symmetry gives rise to a massive pseudo-Goldstone boson. We analyze thermal and nonthermal production of this particle in the early universe, and perform a systematic study of astrophysical and cosmological constraints on its properties. We find that for very suppressed explicit breaking the pseudo-Goldstone boson is a cold dark matter candidate.

Fragile PT-symmetry in a solvable model

Abstract: One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to matching conditions. The result is surprising: An arbitrarily small deformation I→C implies a sudden collapse (i.e., the spontaneous PT-symmetry breaking) of virtually all the spectrum (i.e., up to its low-energy part).

Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

Abstract: We consider a driven diffusive system with two kinds of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems requires placing effective impurities at the boundaries and therefore does not occur in our system. Monte Carlo simulations confirm our results.

Gauge-Assisted Technicolor?

Abstract: It is well known that technicolor models in which the electroweak symmetry is broken by QCD-like strong dynamics at the TeV scale generally predict unacceptably large corrections to low-energy observables. We investigate the models of electroweak symmetry breaking by strong dynamics in which the gauge symmetry is extended to include an arbitrary number of additional SU(2) and U(1) factors. This class of models includes the deconstructed version of the recently proposed five-dimensional "Higgsless" scenario. We conclude that the additional structure present in these theories does not suppress the effects of strongly coupled short-distance physics on the precision electroweak observables. In particular, the possibility that the symmetry breaking is due to QCD-like dynamics is still strongly disfavored by data.

Broken scale invariance in the standard model

Abstract: We introduce Weyl's scale invariance as an additional local symmetry in the standard model of electroweak interactions. An inevitable consequence is the introduction of general relativity coupled to scalar fields a la Dirac and an additional vector particle we call the Weylon. We show that once Weyl's scale invariance is broken, the phenomenon (a) generates Newton's gravitational constant G_N and (b) triggers spontaneous symmetry breaking in the normal manner resulting in masses for the conventional fermions and bosons. The scale at which Weyl's scale symmetry breaks is of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass which is tied to the scale where scale invariance breaks.

Restoration of supersymmetric Slavnov-Taylor and Ward identities in the presence of soft and spontaneous symmetry breaking

Abstract: Supersymmetric Slavnov-Taylor and Ward identities are investigated in presence of soft and spontaneous symmetry breaking. We consider an abelian model where soft supersymmetry breaking yields a mass splitting between electron and selectron and triggers spontaneous symmetry breaking, and we derive corresponding identities that relate the electron and selectron masses with the Yukawa coupling. We demonstrate that the identities are valid in dimensional reduction and invalid in dimensional regularization and compute the necessary symmetry-restoring counterterms.

Mott insulators without symmetry breaking.

Abstract: We present theoretical models, in one and two space dimensions, that exhibit Mott insulating ground states at fractional occupations without any symmetry breaking. The Hamiltonians of these models are nonlocal in configuration space, but local in phase space.

Broken symmetry in density-functional theory: Analysis and cure

Abstract: We present a detailed analysis of the broken-symmetry mean-field solutions using a four-electron rectangular quantum dot as a model system. Comparisons of the density-functional theory predictions with the exact ones show that the symmetry-breaking results from the single-configuration wave function used in the mean-field approach. As a general cure we present a scheme that systematically incorporates several configurations into the density-functional theory and restores the symmetry. This cure is easily applicable to any density-functional approach.