Showing papers on "Four-tensor published in 2010"

The locally covariant Dirac field

Abstract: We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

Stress tensor fluctuations in de Sitter spacetime

Abstract: The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m2/H2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.

Glimmers of a Pre-geometric Perspective

Abstract: Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the possible role of gravity in this framework.

A tensor theory of spacetime as a strained material continuum

Abstract: The classical theory of strain in material continua is reviewed and generalized to spacetime. Strain is attributed to 'external' (matter/energy fields) and intrinsic sources fixing the global symmetry of the universe (defects in the continuum). A Lagrangian for spacetime is worked out, adding to the usual Hilbert term an 'elastic' contribution from intrinsic strain. This approach is equivalent to a peculiar tensor field, which is indeed part of the metric tensor. The theory gives a configuration of spacetime accounting both for the initial inflation and for the late acceleration. Considering also the contribution from matter, the theory is used to fit the luminosity data of type Ia supernovae, giving satisfactory results. Finally the Newtonian limit of the theory is obtained.

Dynamical Backreaction in Robertson-Walker Spacetime

Abstract: The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson-Walker space time. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the sigularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson Walker scale parameter $a(t)$ coupled to the scalar field is finally derived for the case of conformal and also general coupling.

On electromagnetism and generalized energy-momentum tensor of the electromagnetic field in spaces with Finsler geometry

Abstract: By using variational calculus and exterior derivative formalism, we proposed in [30] and [11] a new geometric approach to electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge invariance. Also, for flat pseudo-Finsler spaces, we define a generalized energy-momentum tensor consisting of two blocks, as the symmetrized Noether current corresponding to the invariance of the field Lagrangian with respect to spacetime translations. In curved spaces, one of the blocks of the generalized energy-momentum tensor is obtained by varying the field Lagrangian with respect to the metric tensor and the other one, by varying the same Lagrangian with respect to the nonlinear connection.

Vacuum polarization of the quantized massive scalar field in Reissner-Nordström spacetime

Abstract: The approximation of the renormalized stress-energy tensor of the quantized massive scalar field in Reissner-Nordstroem spacetime is constructed. It is achieved by functional differentiation of the first two nonvanishing terms of the Schwinger-DeWitt expansion involving the coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients [a{sub 3}] and [a{sub 4}] with respect to the metric tensor. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tensor. The approximation to the field fluctuation, , is constructed and briefly discussed.

Vacuum stress-energy tensor of a massive scalar field in a wormhole spacetime

Abstract: The vacuum average value of the stress-energy tensor of a massive scalar field with nonminimal coupling $\ensuremath{\xi}$ to the curvature on the short-throat flat-space wormhole background is calculated The final analysis is made numerically It was shown that the energy-momentum tensor does not violate the null energy condition near the throat Therefore, the vacuum polarization cannot self-consistently support the wormhole

General relativistic spinning fluids with a modified projection tensor

Abstract: An energy-momentum tensor for general relativistic spinning fluids compatible with Tulczyjew-type supplementary condition is derived from the variation of a general Lagrangian with unspecified explicit form. This tensor is the sum of a term containing the Belinfante–Rosenfeld tensor and a modified perfect-fluid energy-momentum tensor in which the four-velocity is replaced by a unit four-vector in the direction of fluid momentum. The equations of motion are obtained and it is shown that they admit a Friedmann–Robertson–Walker space–time as a solution.

Hydrodynamics and global embeddings of Taub-NUT spacetime

Abstract: On Taub-NUT spacetime, we investigate the hydrodynamic properties of perfect fluid spiraling inward toward the spacetime along a conical surface. On the equatorial plane of the Taub-NUT spacetime, we derive the radial equations of motion with eective potentials and the Euler equation for steady-state axisymmetric fluid. Higher dimensional global embeddings are constructed inside and outside the event horizons of the Taub-NUT spacetime. We also study the eective potentials of particles on the Taub-NUT spacetime in terms of the gravitational magnetic monopole strength of the source, the total energy, and the angular momentum per unit rest mass of the particle.