Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

Comment on the Roberts Solution for the Spherically-Symmetric Einstein-Scalar Field Equations

We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.     

General Behaviour of Bianchi VI0 Solutions with an Exponential-Potential Scalar Field

The solutions to the Einstein-Klein-Gordon equations without a cosmological constant are investigated for an exponential potential in a Bianchi VI₀ metric. There exists a two-parameter family of solutions which have a power-law inflationary behaviour when the exponent of the potential, k, satisfies k² < 2. In addition, there exists a two-parameter family of singular solutions for all k² values. A simple anisotropic exact solution is found to be stable when 2 < k².     

Massive, Non-ghost Solutions for the Dirac Field Coupled Self-consistently to Gravity

We present new, massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity. We employ a gauge-theoretic formulation of gravity which automatically identifies the spin of the Dirac field with the torsion of the gauge fields. Homogeneity of the field observables requires that the spatial sections be flat. Expanding and collapsing singular solutions are given, as well as a solution which expands from a singularity before recollapsing. Torsion effects are only important while the Compton wavelength of the Dirac field is larger than the Hubble radius. We study the motion of spinning point-particles in the background of the expanding solution. The anisotropy due to the torsion is manifest in the particle trajectories.     

Interior Weyl-type Solutions to the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitationalfield equations exhibiting a functional relationshipbetween the electric and gravitational potentials arestudied. General results for these metrics are presented which extend previous work of Majumdar. Inparticular it is shown that for any solution of thefield equations exhibiting such a Weyl-typerelationship, there exists a relationship between thematter density, the electric field density and the chargedensity. It is also found that the Majumdar conditioncan hold for a bounded perfect fluid only if the matterpressure vanishes (that is, charged dust). Byrestricting to spherically symmetric distributions ofcharged matter a number of exact solutions are presentedin closed form which generalise the Schwarzschildinterior solution. Some of these solutions exhibitfunctional relations between the electric andgravitational potentials different to the quadratic oneof Weyl. All the non-dust solutions are well-behavedand, by matching them to the Reissner-Nordstromsolution, all of the constants of integration areidentified in terms of the total mass, total charge andradius of the source. This is done in detail for anumber of specific examples. These are also shown tosatisfy the weak and strong energy conditions and manyother regularity and energy conditions that may berequired of any physically reasonable matterdistribution.     

Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

In the present paper we discuss the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields based on sedeonic space-time operators and sedeonic wave functions.     

Letter: Riemannian Metric of the Invariance Quantum Group of the Fermion Algebra

We calculate the bi-invariant metric of FIO(2), the inhomogeneous invariance quantum group of the fermion algebra. We find that this metric is identical to that of the bi-invariant metric of GL(2, R) ⁺ × SU (1, 1). However, the quantum group manifold is restricted to a region of the GL(2, R) manifold.     

Resummation of Mass Terms in Perturbative Massless Quantum Field Theory

The neutral massless scalar quantum field Φ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.      

Zero Point Energy of a Massless Scalar Field in the Cosmic String Space-Time

We consider the ground state energy of a massive scalar field in the space-time of a thick cosmic string in the 2+1 dimensional case for arbitrary angle deficit by using the zeta-function approach. Final numerical calculations were made in the massless case, only. We show that the zero point energy is negative, and for small angle deficit it is proportional to the fourth degree of the deficit.     

Parameter Invariance in Field Theory and the Hamiltonian Formalism

The deparametrization problem for parameter‐invariant Lagrangian densities defined over J¹(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton‐Cartan formalism for such Lagrangians is then introduced and the pre‐symplectic structure of such variational problems is proved to be projectable through the aforementioned projection. Specific examples with physical meaning are also analyzed. 1998 PACS codes. 02.20.Tw Infinite‐dimensional Lie groups, 02.30.Wd Calculus of variations and optimal control, 02.40.Ky Riemannian geometries, 02.40.Ma Global differential geometry, 02.40.Vh Global analysis and analysis on manifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational principles, 11.10.Ef Lagrangian and Hamiltonian approach, 11.10.Kk Field theories in dimensions other than four, 11.25.Sq Nonperturbative techniques; string field theory. 1991 Mathematics Subject Classification. Primary: 58E30 Variational principles; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applications to minimal surfaces (problems in two independent variables), 58G35 Invariance and symmetry properties, 81S10 Geometric quantization, symplectic methods, 83E30 String and superstring theories.     

Wick-Ordered Entire Functions of the Indefinite Metric Free Field

We present a simple and general method for constructing Wick-ordered entire functions of free fields with an indefinite metric, based on using an appropriate generalization of the Paley–Wiener–Schwartz theorem.     

有限温度下无质量场真空图中红外发散的正规化

讨论无质量δ³理论标量场和胶子场三圈真空图中的红外发散和它的正规化,给出了它在D维空间的解析延拓表达式,并讨论了如何分离出交缠发散时的红外发散和共线发散.     

Invariance of the Effective Phase Velocity of a Hydroacoustic Field in the Deep Ocean

Doklady Physics - The distribution of sound pressure and phase gradients is studied in the deep sea along the signal-propagation paths in the near illumination zone (NIZ) and the far illumination...     

On the Gauge Invariance of the Transition Probability of a Charged Particle in Electromagnetic Field

This paper suggests a principle to find a unitary operator U which transforms non-physical quantity,zero-potential Hamiltonian Ho, into true physical quantity UHoU for a charged particle in classical electromagneticfield, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Differentmethods correspond to different unitary operators which satisfy the above-mentioned principle.     

Geometric Structures and Field Equations of Dirac-Lu Space

In this paper, a -invariant Lorentz metric on the Dirac-Lu space is given, and then the geodesic equation is investigated. Finally, we discuss the field equations and find their solutions by the method of separating variables.     

Exact Solitary Wave Solutions of the Coupled Nonlinear Scalar Field Equations

Because of the arbitrary property of the singular manifold, the usual singularity analysis can be extended to a different form. Using a nonstandard truncation approach, five special types of exact solution of the coupled nonlinear scalar field equations are obtained.     

On a Framework for Generating Nonstatic Solutions of the Einstein Field Equations

In this paper we present a simple generalisation of all spherically symmetric static solutions. We present a framework to obtain both anisotropic and isotropic models with and without a barotropic equation of state of the form p = . The nonstaticity in some models necessarily requires a nonzero heat flux which dictates the thermodynamics of our models.     

On the Mean Field Equations of Motion in the Theories with Unstable Vacuum

The problem of finding the mean field equations of motion in the theories with unstable vacuum is considered. The one- and two-loop quantum corrections to classical equations of motion are obtained. It is shown that these quantum corrections are real and causal.