Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

Global Monopole in Kalb–Ramond Background

In recent, S. SenGupta and S. Sur [Phys. Lett. B 502 (2001) 350] have obtained static vacuum solutions of the gravitational field equations in back ground space time with torsion. The torsion is identified with the field strength of a second-rank anti-symmetric tensor field, namely Kalb-Ramond field. In this work, we present the solutions for the metric outside a monopole resulting from the breaking of a global 0(3) symmetry in Kalb-Ramond background. A comparison is made with the corresponding results predicted by general relativity.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Induction of the gravitational constant in an electric field

We investigate the induction of the gravitational constant by a complex scalar field in curved space with the help of the spontaneous symmetry breaking effect. It is shown that the presence of a periodic electric field induces small variations in the Newtonian gravitational constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 98–102, April, 1989.In conclusion, the author expresses thanks to the participants in Professor A. A. Grib's seminar for useful discussions.     

Light quarks mass effect on the color ferromagnet model of the QCD vacuum

We study the effect of quark masses on the energy density of two ferro-magnetic vacua in QCD, corresponding to different vacuum symmetries. In the massless limit the two states have the same energy, while as the quark masses are turned on the state with more symmetry elements becomes the “true” vacuum. The dominant contribution to the energy density splitting is proportional tom ² lnm ²     

Quark strong interactions as a possible mechanism of symmetry breaking in weak interactions

A new mechanism for symmetry breaking is suggested which is connected with the negative contribution of quark loops to the vacuum energy and with the strong interactions of quarks with gluons diminishing this effect. The “gluon mechanism” of symmetry breaking makes it possible to estimate the mass of the heaviest quark (～ 60 GeV) and the mass of the Higgs boson (～ 7 GeV).     

Confront holographic QCD with Regge trajectories of vectors and axial-vectors

By matching the predictions of the Dp–Dq soft-wall model in type II superstring theory with the spectra of vector and axial-vector mesons, we show the dependence of the Regge trajectories parameters on the metric parameters of the model. From the experimental results of Regge parameters for vector mesons, it is found that the D3 background brane with both q=5 and q=7 probe brane and D4 background brane with q=4 probe brane are close to the realistic holographic QCD. We also discuss how to realize chiral symmetry breaking in the vacuum and asymptotic chiral symmetry restoration in high excitation states. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking, and a small negative z ⁴ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.     

A Classical Cosmological Model for Triviality

The aim of this paper is to study the triviality of λ ϕ⁴ theory in a classical gravitational model. Starting from a conformal invariant scalar tensor theory with a self-interaction term λ ϕ⁴, we investigate the effect of a conformal symmetry breaking emerging from the gravitational coupling of the large-scale distribution of matter in the universe. Taking in this cosmological symmetry breaking phase the infinite limit of the maximal length (the size of the universe) and the zero limit of the minimal length (the Planck length) implies triviality, i.e. a vanishing coupling constant λ. It suggests that the activity of the self-interaction term λ ϕ⁴ in the cosmological context implies that the universe is finite and a minimal fundamental length exists.     

Photon Productions in a Gravitational Collapsing

We study a possible gravitational vacuum-effect, in which vacuum-energy variation is due to variation of gravitational field, vacuum state gains gravitational energy and releases it by spontaneous photon emissions. Based on the path-integral representation, we present a general formulation of vacuum transition matrix and energy-momentum tensor of a quantum scalar field theory in curved spacetime. Using analytical continuation of dimensionality of the phase space, we calculate the difference of vacuum-energy densities in the presence and absence of gravitational field. Using the dynamical equation of gravitational collapse, we compute the rate of vacuum state gaining gravitational energy. Computing the transition amplitude from initial vacuum state to final vacuum state in gravitational collapsing process, we show the rate and spectrum of spontaneous photon emissions for releasing gravitational energy. We compare our idea with the Schwinger idea for Sonoluminiescence and contrast our scenario with the Hawking effect.     

Does proton decay follow the exponential law?

Tetrads cause the breakdown of symmetry in gravitational theories. Their vacuum expected values reduce the symmetry of the vacuum from that of the action to what is global Poincaré invariance at ordinary distances. Gravitational theories can be written in terms of rescaled fields in such a way that the Planck mass never appears. The rescaled fields are dimensionless, except for gauge fields and tetrads, both of which acquire the dimension of mass. The empirical distribution of energy throughout spacetime causes the tetrads to assume vacuum expected values of the order of the Planck mass,m _p . Thus the gravitational constant,G=hc/m _p ² , may be viewed not as a fundamental constant, but as a mass scale that is dynamically determined by the large-scale structure of the universe. Generalized tetrads may also break internal symmetries.     

Chaotic inflation in supergravity with Heisenberg symmetry

We propose the introduction of a Heisenberg symmetry of the Kähler potential to solve the problems with chaotic inflation in supergravity, as a viable alternative to the use of shift symmetry. The slope of the inflaton potential emerges from a small Heisenberg symmetry breaking term in the superpotential. The modulus field of the Heisenberg symmetry is stabilized and made heavy with the help of the large vacuum energy density during inflation. The observable predictions are indistinguishable from those of typical chaotic inflation models, however the form of the inflationary superpotential considered here may be interpreted in terms of sneutrino inflation arising from certain classes of string theory.     

Angular Momentum Operator and Fermion-Pair Creation for Non-Abelian Fields

We study the extended structure of non-Abelian dyons, the generalized electromagnetic field and the resulting residual angular momentum in the interior as well as exterior regions of the dyon, and it has been demonstrated that at the dyonic centre there exists no well-defined U(1) charge symmetry and the density of residual angular momentum becomes infinity. The mechanism of creation of a fermionic pair at the dyonic core involving the extremely high density of residual angular momentum has been developed, which leads to baryon-number nonconservation in the presence of non-Abelian dyons. The fermion-number–breaking amplitudes in the presence of a non-Abelian dyon have been analyzed and are not suppressed by exp(– const/e ²). Further, the relevant properties of left-handed fermions in a non-Abelian field has been summarized and the zeroth-order approximation is described. Within this approximation the density of the fermion-number–breaking condensate is found to be O(1), i.e. to be independent of the coupling constant and of the vacuum expectation value of the Higgs field.     

The vacuum structure of light-frontφ 1+1 4 -theory

We discuss the vacuum structure ofφ ⁴-theory in 1+1 dimensions quantised on the light-frontx ⁺=0. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the fieldφ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a meanfield type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way.     

Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids

This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein–Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ^∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428–1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273–294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.     

Flowering to bloom of PeV scale supersymmetric left–right symmetric models

Unified models incorporating right-handed neutrino in a symmetric way generically possess parity symmetry. If this is broken spontaneously, it results in the formation of domain walls in the early Universe, whose persistence is unwanted. A generic mechanism for the destabilization of such walls is a small pressure difference signalled by difference in free energy across the walls. It is interesting to explore the possibility of such effects in conjunction with the effects that break supersymmetry in a phenomenologically acceptable way. This possibility when realized in the context of several scenarios of supersymmetry breaking, leads to an upper bound on the scale of spontaneous parity breaking, often much lower than the GUT scale. In the left–right symmetric models studied, the upper bound is no higher than 10¹¹ GeV but a scale as low as 10⁵ GeV is acceptable.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Vacuum discharge instability at laser initiation of a cathode spot

The dynamics of fast (a current rise time of ≤10¹¹ A/s) laser-induced vacuum discharges with moderate amplitudes of the current (≤10 kA) and voltage (≤20 kV), as well as medium storage energy (20 J), is studied. It is shown experimentally that the initial conditions specified by the energy and duration of laser radiation are a decisive factor governing the discharge dynamics. Two types of beam-plasma instabilities separated in space and time are discovered, and their occurrence conditions are analyzed. The first type of instability, observed early in the discharge, is associated with pinch structures at the front of the cathode jet expanding into a vacuum. The second type arises either at the peak or at the trailing edge of the current pulse and is accompanied by generation of hard (with an energy of ≥100 keV) bremsstrahlung from the anode region. The increase of the hard component energy over the current source potential is attributed to breaking due to plasma erosion.     

有挠量子引力和无鬼de Sitter引力(Ⅱ)——SO(3,2)de Sitter引力的无鬼性

本文利用文献的结果审查了de Sitter引力的粒子内容,发现SO(3,2)de Sitter引力既不含鬼粒子,又不含快子。而SO(4,1)应被排除。SO(3,2)de Sitter理论的粒子内容为m=0,J^P=2⁺,1⁺两种正度规粒子,以及m=2^1/2L^-1(L为de Sitter伪球半径)、J^P=0⁺的正度规粒子。本文还在树图近似下研究了宇宙项所造成的Minkowski真空自发破缺。 关键词：     

Left-right symmetric theories and vacuum domain walls and strings

Theories in which a discrete left-right symmetry is spontaneously broken are expected to lead to the formation of vacuum domain walls. Although the existence of such walls at the present epoch is observationally excluded, we show that such theories are allowed if the discrete symmetry is embedded in a larger continuous symmetry, e.g., SO(10), spontaneously broken at higher temperatures. In this case vacuum strings are formed when the larger symmetry is broken, and these become connected by domain walls when the discrete symmetry is broken. The bounded domain walls tend to shrink, and the system of strings and domain walls decays before its energy density becomes comparable to that of matter. In particular, our arguments allow the symmetry breaking pattern SO(10) → … S[O(6)×O(4)] → SU(3)×SU(2)×U(1) which has been proposed by others.