Topic

# Four-tensor

About: Four-tensor is a research topic. Over the lifetime, 401 publications have been published within this topic receiving 7043 citations.

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TL;DR: In this paper, a new approach to the model-independent description of quantum field theories is introduced, which incorporates in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory.

Abstract: A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory. Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of *-algebras with unital injective *-monomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual Haag-Kastler framework of nets of operator-algebras over a fixed spacetime background-manifold, together with covariant automorphic actions of the isometry-group of the background spacetime, can be re-gained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the time-slice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchy-evolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchy-evolution with respect to the spacetime metric is found to be a divergence-free quantity which has, as will be demonstrated in an example, the significance of an energy-momentum tensor (up to addition of scalar functions) for the locally covariant quantum field theory. Furthermore, we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness.

548 citations

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TL;DR: In this paper, the authors review the debate and its eventual conclusion: no electromagnetic wave energy-momentum tensor is complete on its own, and when the appropriate accompanying energymomentity tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.

Abstract: Almost a hundred years ago, two different expressions were proposed for the energy-momentum tensor of an electromagnetic wave in a dielectric. Minkowski's tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical arguments were advanced in favour of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy-momentum tensor is complete on its own. When the appropriate accompanying energy-momentum tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.

401 citations

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TL;DR: In this paper, the authors studied the physical energy-momentum tensor through which the geometry of spacetime is influenced by a quantized scalar field with conformal coupling to the metric.

Abstract: In preparation for an investigation of whether field-theoretic effects helped to make the early universe become isotropic, we seek to determine the physical (divergence-free) energy-momentum tensor through which the geometry of spacetime is influenced by a quantized scalar field with conformal ("new improved") coupling to the metric. The cosmological models studied are the Kasner-like (type I) metrics (homogeneous, spatially flat, nonrotating, but anisotropic), and also the isotropic Robertson-Walker metrics. The methods employed have previously been expounded in the context of a minimally coupled scalar field and a Robertson-Walker metric. Three divergent leading terms are extracted from an adiabatic expansion of the formal expressions for the expectation values of the energy density and pressures. In the Kasner case a slight reshuffling of the leading terms in the energy density displays all divergences to be proportional to either the metric tensor or a second-order curvature tensor which vanishes when the spacetime is isotropic; hence a finite energy-momentum tensor remains after renormalization of the cosmological constant and one other coupling constant in a generalized Einstein equation. In the Robertson-Walker cases, because of conformal flatness, there is no divergence beyond the usual quartically divergent constant vacuum energy; when the mass is not zero, however, a finite renormalization of the gravitational constant is suggested. The correctness of the methods is tested by considering a coordinate system in which flat spacetime assumes the form of a Kasner universe: The adiabatic definition of particle number and vacuum, which is basic to our expansion and renormalization methods, is seen to be consistent with the usual flat-space concepts.

250 citations

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TL;DR: In this article, the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension is studied.

Abstract: We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

137 citations