Showing papers on "Stress–energy tensor published in 2002"

Lecture notes on holographic renormalization

Abstract: We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown–York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown–York stress energy tensor of an associated AdS spacetime.

Rolling Tachyon

Abstract: We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes Despite the fact that the string field theory action contains infinite number of time derivatives, and hence it is not a priori clear how to set up the initial value problem, the theory contains a family of time dependent solutions characterized by the initial position and velocity of the tachyon field We write down the world-sheet action of the boundary conformal field theories associated with these solutions and study the corresponding boundary states For D-branes in bosonic string theory, the energy momentum tensor of the system evolves asymptotically towards a finite limit if we push the tachyon in the direction in which the potential has a local minimum, but hits a singularity if we push it in the direction where the potential is unbounded from below

Decay of Unstable D-branes with Electric Field

Abstract: Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.

Radion and holographic brane gravity

Abstract: The low energy effective theory for the Randall-Sundrum two brane system is investigated with an emphasis on the role of the non-linear radion in the brane world The equations of motion in the bulk is solved using a low energy expansion method This allows us, through the junction conditions, to deduce the effective equations of motion for the gravity on the brane It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function omega(Psi) = 3 Psi / 2(1-Psi) on the positive tension brane and omega(Phi) = -3 Phi / 2(1+Phi) on the negative tension brane, where Psi and Phi are non-linear realizations of the radion on the positive and negative tension branes, respectively In contrast to the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter, namely, the matters on both positive and negative tension branes, with different effective gravitational coupling constants In particular, the radion disguised as the scalar fields Psi and Phi couples with the sum of the traces of the energy momentum tensor on both branes In the course of the derivation, it has been revealed that the radion plays an essential role to convert the non-local Einstein gravity with the generalized dark radiation to the local quasi-scalar-tensor gravity For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action It is also shown that the quasi-scalar-tensor gravity works as holograms at the low energy in the sense that the bulk geometry can be reconstructed from the solution of the quasi-scalar-tensor gravity

Short distance physics and the consistency relation for scalar and tensor fluctuations in the inflationary universe

Abstract: Recent discussions suggest the possibility that short distance physics can significantly modify the behavior of quantum fluctuations in the inflationary universe, and alter the standard large scale structure predictions. Such modifications can be viewed as due to a different choice of the vacuum state. We show that such changes generally lead to violations of the well-known consistency relation between the scalar to tensor ratio and the tensor spectral index. Vacuum effects can introduce an observable modulation to the usual predictions for the scalar and tensor power spectra.

Lecture Notes on Holographic Renormalization

Abstract: We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime.

Remarks on the distributional Schwarzschild geometry

Abstract: This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a δ-distribution supported at r=0. Using generalized distributional geometry in the sense of Colombeau’s (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues.

Method to compute the stress-energy tensor for the massless spin 1 2 field in a general static spherically symmetric spacetime

Abstract: A method for computing the stress-energy tensor for the quantized, massless, spin $\frac{1}{2}$ field in a general static spherically symmetric spacetime is presented. The field can be in a zero temperature state or a nonzero temperature thermal state. An expression for the full renormalized stress-energy tensor is derived. It consists of a sum of two tensors both of which are conserved. One tensor is written in terms of the modes of the quantized field and has zero trace. In most cases it must be computed numerically. The other tensor does not explicitly depend on the modes and has a trace equal to the trace anomaly. It can be used as an analytic approximation for the stress-energy tensor and is equivalent to other approximations that have been made for the stress-energy tensor of the massless spin $\frac{1}{2}$ field in static spherically symmetric spacetimes.

Sine-Gordon breather form factors and quantum field equations

Abstract: Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. Formulae for the asymptotic behavior of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds and an exact relation between the ``bare'' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy momentum is proven. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.

Generalized Bogoliubov transformation for confined fields: Applications for the Casimir effect

Abstract: The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Casimir effect is calculated for zero and nonzero temperature, and therefore it can be considered as a vacuum condensation effect of the electromagnetic field. This aspect opens an interesting perspective for using this procedure as an effective scheme for calculations in the studies of confined fields, including interacting fields.

Energy-momentum tensor of field fluctuations in massive chaotic inflation

Abstract: We study the renormalized energy-momentum tensor (EMT) of the inflaton fluctuations in rigid space-times during the slow-rollover regime for chaotic inflation with a mass term. We use dimensional regularization with adiabatic subtraction and introduce a novel analytic approximation for the inflaton fluctuations which is valid during the slow-rollover regime. Using this approximation we find a scale invariant spectrum for the inflaton fluctuations in a rigid space-time, and we confirm this result by numerical methods. The resulting renormalized EMT is covariantly conserved and agrees with the Allen-Folacci result in the de Sitter limit, when the expansion is exactly linearly exponential in time. We analytically show that the EMT tensor of the inflaton fluctuations grows initially in time, but saturates to the value ${H}^{2}{H}_{0}^{2},$ where H is the Hubble parameter and ${H}_{0}$ is its value when inflation has started. This result also implies that the quantum production of light scalar fields (with mass smaller or equal to the inflaton mass) in this model of chaotic inflation depends on the duration of inflation and is larger than the usual result extrapolated from the de Sitter result.

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

Abstract: We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c = ?2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.

Stress Energy Tensor in c=0 Logarithmic Conformal Field Theory

Abstract: We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. We analyze the OPE for T, \bar{T} and the logarithmic partners t and \bar{t} for c=0 theories.

Metric-independent analysis of the stress-energy tensor

Abstract: The stress-energy tensor of field theory is defined and analyzed in a geometric setting where a metric is not available. The stress is a linear mapping that transforms the three-form representing the flux of any given property, e.g., charge-current density, to the three-form representing the flux of energy. The example of the electromagnetic stress-energy tensor is given with the additional structure of a volume element.

Decay of Unstable D-branes with Electric Field

Abstract: Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.

Light-cone representation of the spin and orbital angular momentum of relativistic composite systems

Abstract: The matrix elements of local operators such as the electromagnetic current, the energy momentum tensor, angular momentum, and the moments of structure functions have exact representations in terms of light-cone Fock state wavefunctions of bound states such as hadrons. We present explicit light-cone wavefunctions for the two-particle Fock state of the fermion in QED and the Yukawa theory which preserve all the Lorentz properties and give explicit realization of the spin sum rules. The role of orbital angular momentum in understanding the “spin crisis” problem for relativistic systems is clarified. We show how the perturbative structure can be used to simulate much more general bound state systems while preserving all Lorentz properties. We thus obtain a theoretical laboratory to test the consistency of formulae which have been proposed to probe the spin structure of hadrons.

Coframe Energy–Momentum Current. Algebraic Properties

Abstract: The coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy–momentum current witch is covariant under all symmetries of the three-parameter Lagrangian. In this paper we study the relation between the covector valued current and the energy–momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy–momentum as well as the rotational (spin) properties of the field.

Gauge and Non-Gauge Tensor Multiplets in 5D Conformal Supergravity

Abstract: An off-shell formulation of two distinct tensor multiplets, a massive tensor multiplet and a tensor gauge multiplet, is presented in superconformal tensor calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric tensor field, but there is no gauge symmetry in the former, while it is a gauge field in the latter. Both multiplets have 4 bosonic and 4 fermionic on-shell modes, but the former consists of 16 (boson)+16 (fermion) component fields, while the latter consists of 8 (boson)+8 (fermion) component fields.

Symmetry properties under arbitrary field redefinitions of the metric energy-momentum tensor in classical field theories and gravity

Abstract: We derive a generic identity which holds for the metric (i.e. variational) energy?momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy?momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense, a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-2 field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized general relativity, cannot have a gauge invariant metric energy?momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy?momentum tensor in a field-theoretical formulation of gravity must fail.

Vacuum polarization in the spacetime of a charged nonlinear black hole

Abstract: Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of charged black hole being a solution of coupled equations of nonlinear electrodynamics and general relativity is constructed and analysed. It is shown that in a few limiting cases, the analytical expressions relating obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordstr\"{o}m black hole could be derived. A detailed numerical analysis with special emphasis put on the minimal coupling is presented and the results are compared with those obtained earlier for the conformally coupled field. Some novel features of the renormalized stress-energy tensor are discussed.

Geometric Conditions on the Type of Matter Determining the Flat Behavior of the Rotational Curves in Galaxies

Abstract: In an arbitrary axisymmetric stationary spacetime, we determine the expression for the tangential velocity of test objects following a circular stable geodesic motion in the equatorial plane, as function of the metric coefficients. Next, we impose the condition, observed in large samples of disks galaxies, that the magnitude of such tangential velocity be radii independent in the dark matter dominated region, obtaining a constraint equation among the metric coefficients, and thus arriving to an iff (“iff” means: “if and only if.”) condition: The tangential velocity of test particles is radii independent iff the metric coefficients satisfied the mentioned constraint equation. Furthermore, for the static case, the constraint equation can be easily integrated, leaving the spacetime at the equatorial plane essentially with only one independent metric coefficient. With the geometry thus fixed, we compute the Einstein tensor and equate it to an arbitrary stress energy tensor, in order to determine the type of energy-matter which could produce such a geometry. Within an approximation, we deduce a constraint equation among the components of the stress energy tensor. We test in that constraint equation several well known types of matter, which have been proposed as dark matter candidates and are able to point for possible right ones. Finally, we also present the spherically symmetric static case and apply the mentioned procedure to perfect fluid stress energy tensor, recovering the Newtonian result as well as the one obtained in the axisymmetric case. We also present arguments on the need to use GR to study types of matter different than the dust one.

Quantization of Massive Abelian Antisymmetric Tensor Field and Linear Potential

Abstract: We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is the same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.

Belinfante tensors induced by matter-gravity couplings

Abstract: We show that any generally covariant coupling of matter fields to gravity gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent to the canonical energy-momentum tensor of the flat-space theory. For matter fields minimally coupled to gravity our algorithm gives the conventional Belinfante tensor. We establish that different matter-gravity couplings give metric energy-momentum tensors differing by identically conserved tensors. We prove that the metric energy-momentum tensor obtained from an arbitrary gravity theory is on-shell equivalent to the canonical energy-momentum tensor of the flat-space theory.

Positivity and conservation of superenergy tensors

Abstract: Two essential properties of energy–momentum tensors Tμν are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence ∇μTμν = 0. The classical Bel and Bel–Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy–momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla [2, 3] defined a universal algebraic construction which generates a basic superenergy tensor T{A} from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. In [8], we presented a more compact definition of T{A} using the r-direct Clifford algebra ⊗r lp,q. This form for the superenergy tensors allowed us to obtain an easy proof of the DP valid for any dimension. In this paper we include this proof. We explain which new elements appear when we consider the tensor T{A} generated by a non-degree-defined r-fold multivector A and how orthogonal Lorentz transformations and bilinear observables of spinor fields are included as particular cases of superenergy tensors. We find some sufficient conditions for the seed tensor A, which guarantee that the generated tensor T{A} is divergence-free. These sufficient conditions are satisfied by some physical fields, which are presented as examples.

The electromagnetic energy–momentum tensor

Abstract: We clarify the relation between canonical and metric energy–momentum tensors. In particular, we show that a natural definition arises from Noether's theorem which directly leads to a symmetric and gauge invariant tensor for electromagnetic field theories on an arbitrary spacetime of any dimension.

A Characterization of Cosmological Time Functions

Abstract: A characterization of time functions on a spacetime is made by using theMobius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.

Gravitational Field of a Global Monopole in Lyra Geometry

Abstract: We present an approximate solution of global monopole based on Lyra geometry retaining terms of the order 1/3 2 in the energy momentum tensor for a triplet scalar field. Also the gravitational field of the monopole solution has been considered.

Theory of antisymmetric tensor fields

Abstract: It has long been claimed that the antisymmetric tensor field of the second rank is pure longitudinal after quantization. In my opinion, such a situation is quite unacceptable. I repeat the well-known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. Furthermore, on the basis of the Lagrangian formalism I calculate dynamical invariants (including the Pauli-Lubanski vector of relativistic spin for this field). Even on the classical level, the PauliLubanski vector can be equal to zero after applications of well-known constraints. The importance of the normalization is pointed out for the problem of the description of quantized fields of maximal spin 1. The correct quantization procedure permits us to propose a solution to this puzzle in modern field theory. Finally, the discussion of the connection of the Ogievetskĭi-Polubarinov-Kalb-Ramond field and the electrodynamic gauge is presented. PACS: 03.50.-z, 03.50.De, 03.65.Pm, 11.10.-z, 11.10.Ef