Showing papers on "Four-tensor published in 2015"
TL;DR: In this paper, the Hamilton geometry of the phase space of particles whose motion is characterized by general dispersion relations is described, and the expressions for the momentum and position dependent curvatures of spacetime and momentum space are given.
Abstract: We describe the Hamilton geometry of the phase space of particles whose motion is characterized by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and nontrivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$--de Sitter and $\ensuremath{\kappa}$-Poincar\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in general relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
72 citations
TL;DR: In this paper, a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor was provided.
Abstract: We provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions.
49 citations
TL;DR: In this paper, the origin of the nuclear tensor interaction in the covariant energy density functional (EDF) is presented, associated with the Fock diagrams of Lorentz scalar and vector couplings.
Abstract: The origin of the nuclear tensor interaction in the covariant energy density functional (EDF) is presented in this work, associated with the Fock diagrams of Lorentz scalar and vector couplings. With this newly obtained relativistic formalism of the nuclear tensor interaction, more distinct tensor effects are found in the Fock diagrams of the Lorentz scalar and vector couplings, as compared to the Lorentz pseudovector and tensor channels. A unified and self-consistent treatment of both the nuclear tensor and spin-orbit interactions, which dominate the spin-dependent features of the nuclear force, is then achieved by the relativistic models. Moreover, careful analysis of the tensor strengths indicates the reliability of the nuclear tensor interaction in the covariant EDF for exploring the nuclear structure, excitation, and decay modes.
46 citations
TL;DR: In this paper, the expectation value of a scalar operator and of the energy momentum tensor in a conformal field theory was derived from the spectral representation of the 2-point correlation functions of stress energy tensors in Minkowski spacetime.
Abstract: We explore the new technique developed recently in [1] and suggest a correspondence between the N -point correlation functions on spacetime with conical defects and the (N+1)point correlation functions in regular Minkowski spacetime. This correspondence suggests a new systematic way to evaluate the correlation functions on spacetimes with conical defects. We check the correspondence for the expectation value of a scalar operator and of the energy momentum tensor in a conformal field theory and obtain the exact agreement with the earlier derivations for cosmic string spacetime. We then use this correspondence and do the computations for a generic scalar operator and a conserved vector current. For generic unitary field theory we compute the expectation value of the energy momentum tensor using the known spectral representation of the 2-point correlators of stress-energy tensor in Minkowski spacetime.
37 citations
TL;DR: In this article, the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams was explored with the self-consistent tensor effects on the properties of a nuclear matter system.
Abstract: With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of a nuclear matter system. The analysis was performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state, and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach is a natural way to reveal the tensor effects on the nuclear matter system.
28 citations
TL;DR: In this article, the authors introduced spacetimes with semisymmetric energy-momentum tensors and characterized the perfect fluid spacetime with semi-measure tensors.
Abstract: The object of the present paper is to introduce spacetimes with semisymmetric energy-momentum tensor. At first we consider the relation R(X,Y)⋅T=0, that is, the energy-momentum tensor T of type (0,2) is semisymmetric. It is shown that in a general relativistic spacetime if the energy-momentum tensor is semisymmetric, then the spacetime is also Ricci semisymmetric and the converse is also true. Next we characterize the perfect fluid spacetime with semisymmetric energy-momentum tensor. Then, we consider conformally flat spacetime with semisymmetric energy-momentum tensor. Finally, we cited some examples of spacetimes admitting semisymmetric energy-momentum tensor.
26 citations
TL;DR: In this paper, the authors outline a full route from algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with experimental data.
Abstract: The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with experimental data. We give a brief account on the quantization of the free scalar field and its Wick powers in terms of an algebra of functionals on configuration space. Afterwards we demonstrate that there exist states on this algebra in which the energy momentum tensor is qualitatively and quantitatively of the perfect fluid form assumed in the standard model of cosmology up to small corrections. We indicate the potential relevance of one of these corrections for the actively debated phenomenon of Dark Radiation.
11 citations
TL;DR: Li et al. as mentioned in this paper presented a new unified theory of electromagnetic and gravitational interactions by considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime.
Abstract: In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the five-dimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is derived: $
abla_a F^{ab}-\xi R^b_{\;\,a}A^a=-4\pi J^b$ with $\xi=-2$, where $F^{ab}$ is the antisymmetric electromagnetic field tensor defined by the potential vector $A^a$, $R_{ab}$ is the Ricci curvature tensor of the hypersurface, and $J^a$ is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term $\xi R^b_{\;\,a}A^a$, whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. {\bf 48}, 28 (2016)]. Hence, the new unified theory is physically different from the Kaluza-Klein theory and its variants where the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under some conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.
11 citations
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TL;DR: In this article, a non-perturbative determination of the renormalized energy momentum tensor is proposed based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow.
Abstract: We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results.
3 citations
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TL;DR: In this paper, the authors consider two neutral and charged blackfold cases and extract the Brown-York stress energy tensor (tensor of fluid) for all intrinsic metric in the reference spacetime.
Abstract: In this paper we review some properties of higher dimensional black holes. We
take advantages of fluid/gravity duality and obtain the fluid properties of
higher dimensional black holes on the boundary. So we consider two neutral and
charged blackfold cases and extract the Brown-York stress energy tensor (tensor
of fluid). But Brown-York method does not work for all intrinsic metric in the
reference spacetime. Surprisingly, in AAds spacetimes the expectation value of
the stress tensor in the CFT side solves the problem. In our case the neutral
blackfold's spacetime is Ricci-flat. As we know, the compactification of some
directions in any asymptotically AdS black branes corresponds to some kind of
Ricci-flat spacetimes. So by calculating the AAdS form of that metric the dual
renormalized holographic stress tensor has been extracted. This stress tensor
is conserved and traceless, also it is same as perfect fluid.
3 citations
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TL;DR: In this article, the authors present an approach to the problem of the thermodynamical equilibrium of a relativistic fluid in a curved spacetime in the limit of small curvature.
Abstract: We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
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TL;DR: In this paper, the entropy of a spacetime is an expectation value of the entropy operator on a thermo vacuum state, which is the maximal analytic extension of the spacetime studied in this paper.
Abstract: A thermo field dynamics approach for calculating the entropy of a spacetime is suggested. It is exemplified through the Rindler spacetime, the Milne spacetime, the Boulware spacetime, and the Minkowski spacetime with a moving mirror that the entropy of a spacetime is equal to the entropy of a thermo quantum field with the same temperature of the spacetime we study. This in fact suggests an thermo field dynamics approach of calculating the entropy of a spacetime. In this approach, the entropy of a spacetime is an expectation value of the entropy operator on a thermo vacuum state. The thermo vacuum state is the vacuum state on the maximal manifold which is the maximal analytic extension of the spacetime we study.
01 Jan 2015
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TL;DR: In this article, the authors consider two neutral and charged blackfold cases and extract the Brown-York stress energy tensor of fluid, which is conserved and traceless, also it is same as perfect fluid.
Abstract: In this paper we review some properties of higher dimensional black holes. We take advantages of fluid/gravity duality and obtain the fluid properties of higher dimensional black holes on the boundary. So we consider two neutral and charged blackfold cases and extract the Brown-York stress energy tensor of fluid. But Brown-York method does not work for all intrinsic metric in the reference spacetime. Surprisingly, in AAds spacetimes the expectation value of the stress tensor in the CFT side solves the problem. In our case the neutral blackfold's spacetime is Ricci-flat. As we know, the compactification of some directions in any asymptotically AdS black brane corresponds to a Ricci-flat spacetime. So by calculating the AAdS form of that metric the dual renormalized holographic stress tensor has been extracted. This stress tensor is conserved and traceless, also it is same as perfect fluid.
TL;DR: In this paper, a simple Lagrangian density constructed from combination of the standard Ricci tensor and a new tensor field that appears due to the immersion, leads to gravitational equations in which the vacuum energy gravitates with a different cosmological strength as in Phys. Rev.
Abstract: We formulate Eddington's affine gravity in a spacetime which is immersed in a larger eight dimensional space endowed with a hypercomplex structure. The dynamical equation of the first immersed Ricci-type tensor leads to gravitational field equations which include matter. We also study the dynamical effects of the second Ricci-type tensor when added to the Lagrangian density. A simple Lagrangian density constructed from combination of the standard Ricci tensor and a new tensor field that appears due to the immersion, leads to gravitational equations in which the vacuum energy gravitates with a different cosmological strength as in Phys. Rev. D {\bf 90}, 064017 (2014), rather than with Newton's constant. As a result, the tiny observed curvature is reproduced due to large hierarchies rather than fine-tuning.
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TL;DR: In this article, a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space is introduced, and by forcing a condition of holomorphism a Minkowski-type spacetime emerges, from which special relativity, gravitation and also the whole Maxwell theory of electromagnetic fields arises.
Abstract: Introducing a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space, and by forcing a condition of holomorphism, a Minkowski-type spacetime emerges, from which special relativity, gravitation and also the whole Maxwell theory of electromagnetic fields arises.
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TL;DR: The main object of as discussed by the authors is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasi-Einstein, generalized Roter type, $Ein(3)$ manifold satisfying $R.
Abstract: Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasi-Einstein, generalized Roter type, $Ein(3)$ manifold satisfying $R.R = Q(S,R)$, $C\cdot C = \frac{2a^2}{3} Q(g,C)$, and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between G\"odel spacetime and Som-Raychaudhuri spacetime.
TL;DR: In this paper, the authors deal with Heisenberg spacetime representing the component of Faraday tensor and express some interesting relations about faraday tensors in the spacetime.
Abstract: The present study deals with Heisenberg spacetime representing the component of Faraday tensor. We express some interesting relations about Faraday tensor in the Heisenberg spacetime. Finally, we illustrate the components of Faraday tensor in the Heisenberg spacetime.
TL;DR: In this article, a model of the universe based on energetic spacetime (zero point energy) is expanded, and the energy density of spacetime is calculated using only general relativity and acoustic equations.
Abstract: A model of the universe based on energetic spacetime (zero point energy) is expanded. The energy density of spacetime is calculated using only general relativity and acoustic equations. This energetic spacetime is shown to possess the properties required to be the new aether (Lorentz invariance, quantization of angular momentum, impedance, and quantum mechanical energy density.) The contradictory wave-particle duality properties of a photon are resolved by a model where a photon is a wave propagating in energetic spacetime but appearing to have particle properties because it possesses quantized angular momentum. Compton scattering and the photoelectric effect are examined and found to be compatible with the proposed wave-based photon model.
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TL;DR: In this article, the first complete parametrization for the matrix elements of the generic light-front gauge-invariant energy-momentum tensor was presented.
Abstract: We present the first complete parametrization for the matrix elements of the generic light-front gauge-invariant energy-momentum tensor, derive the expressions giving separately the spin and orbital angular momentum of quarks and gluons as probed in high-energy scattering experiments, and discuss the relations with two-parton generalized and transverse-momentum dependent distributions. As a by-product, we recovered the Burkardt sum rule, clarified its physical meaning and obtained similar new sum rules for higher-twist distributions.
TL;DR: In this paper, a non-electromagnetic wavefield is constructed that shows covariance properties under a Lorentz-type of transformation of the relevant space-time coordinates and associated field and source quantities in affine (N + 1 ) -spacetime.