Showing papers on "Stress–energy tensor published in 1977"
TL;DR: In this article, a generalized zeta function was proposed to regularize quadratic path integrals on a curved background spacetime, which can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time.
Abstract: This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator that appears in the action integral. The zeta function is a meromorphic function and its gradient at the origin is defined to be the determinant of the operator. This technique agrees with dimensional regularization where one generalises ton dimensions by adding extra flat dimensions. The generalized zeta function can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time. Using the asymptotic expansion for the heat kernel, one can deduce the behaviour of the path integral under scale transformations of the background metric. This suggests that there may be a natural cut off in the integral over all black hole background metrics. By functionally differentiating the path integral one obtains an energy momentum tensor which is finite even on the horizon of a black hole. This energy momentum tensor has an anomalous trace.
1,251 citations
TL;DR: In this paper, a finite energy-momentum tensor is constructed in an asymptotically free non-Abelian gauge theory with massive fermions (quarks), and an explicit formula is found for the trace when inserted into a gauge-invariant Green function.
260 citations
TL;DR: In this article, the theory of quantized gravitational wave perturbations in the three types of Robertson-Walker universes was considered and the spectrum of gravitons produced by a power-law expansion of the universe was calculated.
Abstract: We consider the theory of quantized gravitational wave perturbations in the three types of Robertson-Walker universes. In a gauge analogous to the Coulomb gauge in electrodynamics it is possible to identify and quantize the independent degrees of freedom of the graviton field. The resulting theory is equivalent to that for a pair of massless, minimally coupled scalar fields in the same background space-time. As an application of the formalism, we calculate the spectrum of gravitons produced by a power-law expansion of the universe and show that it has no divergences.
202 citations
TL;DR: In this article, the authors investigate infrared divergences of expectation values of products of field operators in a class of curved space-times, and show that such divergence cannot evolve dynamically in these models from initial conditions which are free of them.
Abstract: We investigate infrared divergences of expectation values of products of field operators in a class of curved space-times. The massless minimally coupled scalar field and the linearized gravitational field, quantized on a subset of spatially flat Robertson-Walker background metrics, have such divergences for an apparently natural choice of state vectors. For those states which give a large infrared contribution to the energy-momentum tensor, we show that these metrics cannot be self-consistent solutions of Einstein's equations. Finally, we show that such divergences cannot evolve dynamically in these models from initial conditions which are free of them. These divergences provide one possible criterion for limiting the acceptable choices of state vectors in curved space-time.
195 citations
TL;DR: The Noether operator as mentioned in this paper is a generalization of the canonical stress energy tensor, and it has been shown to be an extremum-energy maximization operator for field theories.
188 citations
TL;DR: In this article, the authors compute the stress-tensor vacuum expectation value of a massive, scalar quantum field coupled to the metric of an arbitrary classical gravitational field, which is defined by a dimensionally continued, proper-time representation.
Abstract: We compute the stress-tensor vacuum expectation value of a massive, scalar quantum field that is coupled to the metric of an arbitrary classical gravitational field. The renormalized tensor is defined by a dimensionally continued, proper-time representation. The stress tensor is calculated for arbitrary dimension in a potentially conformal-invariant manner so that its trace is formally proportional to the square of the scalar-field mass with this trace vanishing as the scalar field becomes massless. However, the renormalized stress tensor violates this formal identity with its trace containing additional, anomalous terms. These finite-trace anomalies are intimately related to the infinite counterterms that must be put into the action to make the stress tensor finite.
144 citations
TL;DR: In this article, the authors study the regularization of the stress energy tensor for massless vector and massless and massive scalar particles propagating in a general background metric, using covariant point-separation techniques.
132 citations
TL;DR: In this paper, the point-split stress tensor of a conformally invariant scalar field in a spatially flat Robertson-Walker geometry is derived from the short-distance behavior of the corresponding operator products evaluated at separated points.
127 citations
TL;DR: In this article, the authors derived the unique local vacuum stress tensor for electromagnetic, neutrino and massless scalar fields propagating in a Robertson-Walker background spacetime, which was used to compute the numerical coefficients of the conformal trace anomalies from the known values of the Casimir energy in the Einstein universe.
Abstract: We derive the unique, local vacuum stress tensor for electromagnetic, neutrino and massless scalar fields propagating in a Robertson─Walker background spacetime. The result is used to compute the numerical coefficients of the conformal trace anomalies from the known values of the Casimir energy in the Einstein universe.
46 citations
TL;DR: In this paper, the exact vacuum polarization 4-tensor in the presence of a static magnetic field is calculated by a method due to Svetozarova and Tsytovich (1962).
Abstract: The exact vacuum polarization 4-tensor in the presence of a static magnetic field is calculated by a method due to Svetozarova and Tsytovich (1962). The Hermitian part of the tensor is explicitly renormalized and the anti-Hermitian part of the tensor is found to be finite and gauge invariant. An alternative method for calculating the vacuum polarization tensor is developed using the relation between the anti-Hermitian part of the tensor and the probability of emission and absorption of a photon by an electron in a static magnetic field.
38 citations
TL;DR: In this paper, a Lagrangian is obtained by deriving the path-integral representation of the diffusion process, which can be applied, e.g., to nonequilibrium thermodynamics and to quantized motion in general relativity.
Abstract: A Lagrangian is obtained by deriving the path-integral representation of the diffusion process. It can be applied, e.g., to nonequilibrium thermodynamics and to quantized motion in general relativity. In second quantization it is shown to lead to a particularly well-behaved energy-momentum tensor as a source of gravity.
TL;DR: In this paper, the order-cap alpha-quantum-electrodynamic modifications to the photon stress tensor were calculated using the finite, causal methods of source theory, in agreement with those of Berends and Gastmans, who used dimensional regularization.
Abstract: The order-..cap alpha.. quantum-electrodynamic modifications to the photon stress tensor are calculated using the finite, causal methods of source theory. The results are in agreement with those of Berends and Gastmans, who used dimensional regularization. Although the corrected stress tensor is conformally invariant, a ''trace anomaly'' does appear as a consequence of gravitational and electromagnetic gauge invariance.
TL;DR: In this paper, the authors applied two-dimensional stress energy regularization techniques to the two dimensional analog of the Reissner-Nordstrom family of black-hole metrics and calculated the stress energy tensor in all cases containing the thermal radiation discovered by Hawking.
Abstract: The recently developed two-dimensional stress-energy regularization techniques are applied to the two-dimensional analog of the Reissner-Nordstr\"om family of black-hole metrics. The calculated stress-energy tensor in all cases contains the thermal radiation discovered by Hawking. Implications for the evolution of the interior of a charged black hole are considered. The calculated stress-energy tensor is found to diverge on the inner, Cauchy, horizon. Thus the effect of quantum mechanics is to cause the Cauchy horizon to become singular. The stress-energy tensor is also calculated for the "most reasonable" two-dimensional analog of the Kerr-Newman family of black-hole metrics. Although the analysis is not as rigorous as in the Reissner-Nordstr\"om case, it appears that the correct value for the Hawking radiation also appears in this model.
TL;DR: The relativistic conservation of intrinsic hypermomentum fits the observed regularities of hadrons: SU(6) ( approximately spin independence), scaling, and complex-J trajectories, which correspond to volume-preserving deformations (confinement?) exciting rotational bands.
Abstract: We demonstrate the existence of double-valued linear (infinite) spinorial representations of the group of general coordinate transformations. We discuss the topology of the group of general coordinate transformations and its subgroups GA(nR), GL(n,R), SL(nr) for n = 2,3,4, and the existence of a double covering. We present the construction of band-spinor representations of GL(n,R) in terms of Harish-Chandra modules.
It is suggested that hadrons interact with gravitation as band-spinors of that type. In the metric-affine extension of general relativity, the hadron intrinsic hypermomentum is minimally coupled to the connection, in addition to the coupling of the energy momentum tensor to the vierbeins. The relativistic conservation of intrinsic hypermomentum fits the observed regularities of hadrons: SU(6) (∼ spin independence), scaling, and complex-J trajectories. The latter correspond to volume-preserving deformations (confinement?) exciting rotational bands.
TL;DR: In this article, the authors discuss the absence of stationary source-free solutions and the positive energy problem in general relativity at the linearized level in terms of the Bel-Robinson tensor, and raise the possibility that there may exist stationary solutions to the full Einstein equations in five dimensions.
Abstract: The absence of stationary source-free solutions and the positive energy problem in general relativity are discussed, at the linearized level, in terms of the Bel-Robinson tensor. The possibility is raised that there may exist stationary solutions to the full Einstein equations in five dimensions.
TL;DR: In this article, it was shown that the spin-spin contact interactions, which are characteristic of the Einstein-Carton-Sciama-Kibble theory of gravitation, are attractive for the case of a totally antisymmetric spin angular momentum density tau/sub i j k/ which is appropriate for the Dirac field.
Abstract: Kerlick has obtained the unexpected result that the spin-spin contact interactions, which are characteristic of the Einstein-Carton-Sciama-Kibble theory of gravitation, are attractive for the case of a totally antisymmetric spin angular momentum density tau/sub i j k/ which, in particular, is appropriate for the Dirac field. Using our previous techniques, where the emphasis is on the use of Lagrangian densities as opposed to energy-momentum densities, we present a simple and explicit verification of this result.
TL;DR: In this article, the authors used covariant point splitting to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time.
Abstract: The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case.
TL;DR: In this article, the stress energy tensor of a massless scalar field is calculated for a general two-dimensional black hole, and it is shown that the black hole always emits blackbody radiation with temperature proportional to the surface gravity.
Abstract: The stress-energy tensor of a massless scalar field is calculated for a "general" two-dimensional black hole. The black hole is found to always emit blackbody radiation with temperature proportional to the surface gravity of the black hole.
TL;DR: In this paper, a uniqueness theorem for the geometric part of the field equations is proven and a Lagrangian is determined which is uniquely specified by dimensional analysis within the context of scalar-metric-torsion gravitational theories.
Abstract: The techniques of dimensional analysis and of the theory of tensorial concomitants are employed to study field equations in gravitational theories which incorporate scalar fields of the Brans-Dicke type. Within the context of scalar-metric gravitational theories, a uniqueness theorem for the geometric (or gravitational) part of the field equations is proven and a Lagrangian is determined which is uniquely specified by dimensional analysis. Within the context of scalar-metric-torsion gravitational theories a uniqueness theorem for field Lagrangians is presented and the corresponding Euler-Lagrange equations are given. Finally, an example of a scalar-metric-torsion theory is presented which is similar in many respects to the Brans-Dicke theory and the Einstein-Cartan theory.
TL;DR: In this article, the stress tensor is calculated for an ideal type II superconductor in the mixed state, where the structural changes in the vortex system caused by transport current are taken into account.
Abstract: The stress tensor is calculated for an ideal type II superconductor in the mixed state. The present stress tensor differs from Josephson's expression insofar as it takes into account the structural changes in the vortex system caused by transport current. The corresponding volume force is not only the Lorentz forcej × B; there are additional terms arising from the gradient of the number density of vortices and from the tension of the vortex lines. It turns out, in particular, that in some geometries a persistent transport current can exist and not be parallel to the magnetic inductionB. The general expressions are applied to the cases of a slab in longitudinal and transverse external magnetic fields.
TL;DR: In this paper, a Lagrangian density, quadratic in Riemann's curvature tensor and Cartan's torsion tensor, is introduced, which makes possible the propagation of gravitational energy in the absence of matter.
Abstract: Gravitation is considered as a gauge field within the formalism of Utiyama and Kibble. In empty space-time a Lagrangian density, quadratic in Riemann's curvature tensor and in Cartan's torsion tensor, is introduced. The equations of motion are coupled differential equations for the curvature and torsion tensors. The spin of the torsion field behaves as a curvature source and the energy of both fields acts as a torsion source. Each field has an energy tensor, similar to the Maxwell tensor of electrodynamics, vanishing in a torsionless space. It thus appears that the torsion of space-time is a geometric property that makes possible the propagation of gravitational energy in the absence of matter.
TL;DR: In this paper, it was shown that the angular distributions of the polarization transfer coefficients contain new complementary information on the tensor part of the deuteron-nucleus interaction which cannot be obtained solely from tensor analyzing power measurements.
TL;DR: In this article, a generalized variational principle for the simultaneous determination of the behavior of both the electromagnetic and the dynamical gravitational fields is used to obtain an alternative energy-momentum tensor density ϑhj.
Abstract: When the field tensor of an electromagnetic field admitting both electric and magnetic charge distributions is expressed in terms of a Clebsch representation, the extended Maxwell equations in the presence of a given gravitational field are derivable from an invariant variational principle in which the Clebsch potentials play the role usually assumed by the classical 4‐potentials. The corresponding Lagrange density gives rise in a unique manner to a symmetric tensor density Thj, which displays some of the properties normally associated with the energy–momentum tensor density of the electromagnetic field. However, this interpretation may be in conflict with the generally accepted expression for the modified Lorentz force. Accordingly an alternative energy–momentum tensor density ϑhj is derived which does not suffer from this drawback. However, when a generalized variational principle for the simultaneous determination of the behavior of both the electromagnetic and the dynamical gravitational fields is int...
TL;DR: In this article, the authors derived a theorem on the coupling of the trace of the energy-momentum tensor to two photons, and proved that the trace can be represented by two photons.
Abstract: We derive a theorem on the coupling of the trace of the energy-momentum tensor to two photons.
TL;DR: In this article, it was shown that a homothetic conformal transformation of the metric tensor is both necessary and sufficient to ensure that a source-free non-null electromagnetic field in four dimensions undergoes a duality rotation leaving its energy-momentum tensor invariant.
Abstract: A homothetic conformal transformation of the metric tensor is both necessary and sufficient to ensure that a source-free non-null electromagnetic field in four dimensions undergoes a duality rotation leaving its energy-momentum tensor invariant. For null electromagnetic fields the condition is sufficient but not necessary. The result suggests that vacuum Einstein-Maxwell space-times exist which admit groups of homothetic motions. If the order of such a group is greater than unity it must be associated with isometry transformations of the metric tensor other than those obtained as a special case of the conformal group.
TL;DR: In this article, a symmetrical locally conserved energy-momentum tensor whose trace vanishes is considered, and it is shown that there are no other combinations of the position variables x and the EMT whose divergence vanishes except the well-known currents of translations, four-dimensional Lorentz rotations as well as con- formal and dilatational transformations.
TL;DR: In this article, it was shown that the stress tensor for a superfluid contains a quite new off-diagonal term occurring also in the entropy equation and that the new term should be added to the static pressure to give the total pressure.
Abstract: From an approach based on reduced density matrices it follows that the stress tensor for a superfluid contains a quite new off-diagonal term occurring also in the entropy equation. Examination of this problem on the basis of the theory proposed by Bogoliubov suggests that the new term should be added to the static pressure to give the total pressure. In addition, it is demonstrated that the second derivative of free energy with respect to volume and the square of the superfluid velocity do not commute.
TL;DR: In this paper, two solutions with the energy-momentum tensor of an ideal fluid are obtained on the basis of theorems proved earlier by the author on the possibility of constructing new solutions of the Einstein equations from solutions already known by means of conformal mapping.
Abstract: Two solutions with the energy-momentum tensor of an ideal fluid are obtained on the basis of theorems proved earlier by the author on the possibility of constructing new solutions of the Einstein equations from solutions already known by means of conformal mapping. The first of these solutions is a conformal correspondent to the De Sitter solution, and the second corresponds to the class of Friedman solutions. The explicit form of the metrics of the new solutions and of the parameters of the energy-momentum tensor is written out, and the properties of the corresponding space-times are also investigated.
TL;DR: In this paper, the instanton tunnelling amplitude induces a nonperturbative violation of scale invariance which can be understood in terms of the anomaly in the trace of the stress energy tensor.