Wightman function and vacuum polarization in models with non-trivial topology in the presence of boundaries

Wightman function and the vacuum expectation value of the scalar field squared are studied in models with a compact subspace in the presence of parallel plane boundaries, on which the field obeys Robin boundary conditions. By means of the generalized Abel-Plana summation formula we have explicitly extracted from the vacuum expectation values the parts induced by the boundaries. As a simple example, a one-dimensional internal space is considered compactified on a circle.     

Casimir forces in models with non-trivial topology

The Casimir forces, acting on the parallel plates in models with the compact subspace are investigated for the case of a scalar field. The field obeys the Robin boundary conditions on the plates. Depending on the values of the coefficients in the boundary conditions, the forces can be either attractive or repulsive. In models with a homogeneous compact subspace, they are the same for both the plates. In special cases of the Dirichlet and Neumann boundary conditions, the Casimir forces are attractive. Proceeding from general results, two particular cases with the subspaces S¹ and S² are considered.     

Vacuum expectation values of the energy-momentum tensor in two dimensions

A general form of the vacuum expectation values of the components of the energy-momentum tensor is derived in the case of static two-dimensional spacetime. Conditions for the regularity of the energy-momentum tensor are set. A generalized formula for the black hole temperature originally found by Hawking is given. The regularity of the energy-momentum tensor in the presence of more than one horizon is investigated.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland.     

Vacuum averages of the energy-momentum tensor of quantized fields on manifolds of various topology and geometry. II

The analytic dependences of the vacuum averages of the energy-momentum tensor on geometry and topology are found for scalar, electromagnetic, and massless gluon fields in bounded three-dimensional manifolds. Application of the results obtained to the bag model in the theory of hadrons is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 51–54, September, 1979.The authors are grateful to A. A. Grib for many useful discussions.     

Vacuum means of energy-momentum tensor of quantized fields on manifolds of different topology and geometry. I

We consider the topological and geometric relations of the energy-momentum tensor of zero-point vacuum vibrations of a scalar field in two-dimensional manifolds. It is shown that the energy density can change sign under continuous deformation of the region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 88–93, July, 1979.The authors are indebted to A. A. Grib and to the participants in the Leningrad gravitational seminar, which he heads, for their useful discussion.     

Vacuum expectation values of the energy-momentum tensor of quantized fields on manifolds of different topology and geometry. IV

A new method is proposed for calculating the vacuum energy-momentum tensor on bounded manifolds that does not require a cutoff or other artificial devices. The impenetrable boundaries are replaced by a family of localized potentials which depend on a parameter , the boundary condition corresponding to impenetrability being obtained in the limit . The Casimir effect in the case of two parallel plates is considered in detail.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 78–82, February, 1981.     

Space-times with covariant-constant energy-momentum tensor

It is shown that a general relativistic space-time with covariant-constant energy-momentum tensor is Ricci symmetric. Two particular types of such general relativistic space-times are considered and the nature of each is determined.     

The connection between the energy-momentum tensor and the tensor field in presence of a mass gap

The conditions under which a tensor field can be regarded as an energy-momentum tensor are discussed. The problem connected with dilatational and conformal symmetries are exhibited.     

Classical string dynamics with non-trivial topology

The possibility of branching processes for classical strings is investigated on the basis of the Nambu-Goto action. We parametrize the world sheet by a Riemann surface M and introduce a degenerate, semi-Riemannian metric η on M. Well-known results about the conformal group Diff(S¹) × Diff(S¹) are generalized to the case of (M, η). We provide an infinite dimensional Hamiltonian setting for branching processes of strings. Finally, the classical background for the theory of quantum strings as developed by Krichever and Novikov is discussed within this classical framework.     

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

Generalized, or “power-law”, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.     

On the new improved energy-momentum tensor

The requirement of the conformal covariance of the theory in the limit of vanishing masses leads to improving terms in energy-momentum tensor. Some consequences of the fact are briefly summarized.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Classical solutions and the energy-momentum tensor

A hyperelliptic two-meron solution of the massless scalar φ^N theory in $\text{n =}\text{2N}\text{(N ? 2)}$ Euclidean dimensions is given. This solution (which interpolates between the two-meron solution and the instanton solution of this theory) is used to illustrate several theory-independent statements which can be made about the energy-momentum tensor for instanton, meron and elliptic meron solutions of all scale invariant classical field theories.     

An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

The algebra of the energy-momentum tensor and the Noether currents in classical non-linear sigma models

The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor , the Noether currentj associated with the global symmetry of the theory and the composite fieldj appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives ofj andj, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central chargec=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type construction.Supported by the Deutsche Forschungsgemeinschaft, Contract No. Ro 864/2-1Supported by the Studienstiftung des Deutschen Volkes     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Vacuum expectation values of the energy-momentum tensor of quantized fields on manifolds with different topologies and geometries. III

In a continuation of the earlier work [1, 2] into vacuum effects of quantized fields on bounded manifolds, the case of a spinor field is considered. The question of the boundary conditions for the Dirac equation is studied. Analytic results are obtained for a number of configurations. A comparison is made with the case of boson fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–13, July, 1980.     

New energy-momentum tensor in relativistic gravitation theory

Expressions for a new canonical energy-momentum tensor and an internal angular momentum of the gravitational field are derived in the context of bimetric relativistic gravitation theory based on the variational principle. A system of relations for the determining parameters of the gravitational field and matter involving, in particular, the continuity condition for the energy-momentum flux density is formulated on the discontinuity surface. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–58, April, 2006.