Symmetry Breaking Due to Conformally Invariant Scalar Field

In the framework of Weyl invariant gravitational field theory including torsion coupled to a scalar field with arbitrary selfinteraction it will be shown that any solution of such a generalized Goldstone model contains the conformally invariant field of a massless scalar particle. Due to this fact it may happen that dynamical symmetry breaking becomes impossible.     

Conformally Flat Spacetimes and Weyl Frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordstr?m scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.     

A conformai,symmetry broken model for gravity

Starting from Padmanabhan's fully conformally invariant action, we obtain gravity as a spontaneously broken theory. Newton's constant and the cosmological constant follow from the breakdown of the conformal symmetry at the tree approximation. For small oscillation of the scalar field about the fundamental state, the matter field degenerates into two decoupled fields.     

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.     

Some remarks on zeta function regularization in curved space-times

The question of to what extent zeta function regularization respects the invariances of a quantum field theory in a background gravitational field is investigated. It is shown that zeta function regularization provides a generalization to curved space-time of analytic propagator regularization which is known not to respect gauge invariance. Furthermore, a study of the regularized stress tensor of a conformally invariant scalar field indicates that both conformai and general coordinate invariance are violated.     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

Ward identities and radiative corrections in QED with conformal gauge

A model of QED with conformally invariant gauge is considered. This gauge, being essentially nonlocal, is written in a local form by means of two nonphysical scalar fields. Using the BRST symmetry and the additional residual symmetry, a system of Ward identities is derived. These Ward identities are applied to prove the renormalizability of the model as well as to investigate the radiative corrections. A new class of conformal anomalies arises, connected with the absence of radiative corrections to the propagators including auxiliary fields.     

Induced gauge theory on a noncommutative space

We consider a scalar φ⁴ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action, using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model. PACS 11.10.Nx; 11.15.-q     

Conformal invariance and torsion in general relativity

We study a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition g =0. A scalar field is added to the theory, and a conformally invariant action integral, linear in the curvature tensor, is defined. The linear connections emerging from the variational principle contain torsion that is related to a propagating spin-1 vector field, identified as the electromagnetic gauge potential. We obtain a set of conformally invariant equations for the metric field, and conclude that Einstein's equations arise from a particular choice of gauge. Finally, spin-1/2 fields are introduced by means of the vierbein formalism, and the qualitative features of the theory are maintained.     

Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Self-gravitating scalar field with cubic nonlinearity

For a self-gravitating massless conformally invariant scalar field a solution is obtained to the Einstein equations for which the geometry of space-time remains arbitrary. For a scalar field with cubic nonlinearity, a static solution to the Einstein equations possessing plane symmetry is found. A cosmological model with nonlinear scalar field in the class of conformally flat Friedmann metrics is investigated. An example is given of an exact solution to the equations of the gravitational field with singularity in the infinite past.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 18–22, December, 1980.     

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.     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

大尺度有效引力的E(2)规范理论模型

微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.     

The T-dual symmetries of a bosonic string

We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world-sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.     

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

In this paper, we investigate the generalized Saez–Ballester scalar–tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

A new approach to spontaneously broken conformal symmetry

In this paper we present a new method for constructing theories of gravitation which exhibit spontaneously broken conformal symmetry. It does not require introducing nongeometric terms (i.e., auxiliary gauge fields or potential terms for the conformal field) into the Lagrangian. It is based on a theory which initially is locally both Lorentz invariant and Weyl gauge invariant inD dimensions. It is shown that, if the field Lagrangian contains terms quadratic in curvature in addition to the Ricci scalar, then the field equations allow both the dilation field and some connection components to have nonvanishing vacuum values. Both Lorentz and Weyl symmetries are thereby broken simultaneously.     

Inconsistencies of the U(1) Theory of Electrodynamics: Stress Energy Momentum Tensor

The internal gauge space of electrodynamics considered as a U(1) gauge field theory is a scalar. This leads to the result that in free space, and for plane waves, the Poynting vector and energy vanish. This result is consistent with the fact that U(1) gauge field theory results in a null third Stokes parameter, meaning again that the field energy vanishes in free space. A self consistent definition of the stress energy momentum tensor is obtained with a Yang Mills theory applied with an O(3) symmetry internal gauge space. This theory produces the third Stokes parameter self consistently in terms of the self-dual Evans-Vigier fields B(3).