Stress tensor for massive fields on flat spaces of spatial topology

Langlois, Paul

doi:10.1088/0264-9381/22/19/022

Cited by 4 publications

(11 citation statements)

References 15 publications

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“…Boundary conditions enter because our result could equally be stated as the infimum as h varies over the range of T n in L 1 , all elements of which obey the specific boundary conditions we have imposed. In fact, (17) was used to obtain a result quite similar in spirit to our main result: namely, that While the strategy employed in [6] overlaps in part with ours, the key portions of the two arguments (leading to (17) in [6], or our bounds on λ n ) are quite different.…”

Section: Results For Other L P Spacesmentioning

confidence: 60%

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Mass dependence of quantum energy inequality bounds

Eveson

Fewster

2007

Journal of Mathematical Physics

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In a recent paper [J. Math. Phys. 47 082303 (2006)], Quantum Energy Inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian spacetime regions. Here, we refine this analysis for massive fields, obtaining more stringent bounds which decay exponentially in the mass. At the technical level this involves the determination of the asymptotic behaviour of the lowest eigenvalue of a family of polyharmonic differential equations, a result which may be of independent interest. We compare our resulting bounds with the known energy density of the ground state on a cylinder spacetime. In addition, we generalise some of our technical results to general L p -spaces and draw comparisons with a similar result in the literature.

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Section: Results For Other L P Spacesmentioning

confidence: 60%

“…Consider the cylinder spacetime (N, η) formed by periodically identifying four-dimensional Minkowski space under a translation in the z-direction. The ground state energy density in this spacetime, for the quantized minimally coupled scalar field of mass m is [23,17]…”

Section: Example: Cylinder Spacetimesmentioning

confidence: 99%

Mass dependence of quantum energy inequality bounds

Eveson

Fewster

2007

Journal of Mathematical Physics

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“…Let us note that the massless QEI bound also provides a lower bound on the ground state energy densities of massive scalar fields in these spacetimes. Consistency here is seen from the fact that the mass diminishes the magnitude of the energy density [51] (note the misprints in [51] noted in [52] which do not, however, affect the final result).…”

Section: A Two-dimensional Timelike Cylindermentioning

confidence: 55%

Quantum energy inequalities and local covariance. I. Globally hyperbolic spacetimes

Fewster

Pfenning

2006

Journal of Mathematical Physics

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We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covariance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions. Local covariance permits us to place constraints on the renormalised stress-energy tensor in one spacetime using QEIs derived in another, in subregions where the two spacetimes are isometric. This is of particular utility where one of the two spacetimes exhibits a high degree of symmetry and the QEIs are available in simple closed form. Various general applications are presented, including a priori constraints (depending only on geometric quantities) on the ground-state energy density in a static spacetime containing locally Minkowskian regions. In addition, we present a number of concrete calculations in both two and four dimensions which demonstrate the consistency of our bounds with various known ground-and thermal state energy densities. Examples considered include the Rindler and Misner spacetimes, and spacetimes with toroidal spatial sections. In this paper we confine the discussion to globally hyperbolic spacetimes; subsequent papers will also discuss spacetimes with boundary and other related issues.

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“…Finally let us consider M − [9,10,31] which is a quotient of Minkowski space (or of M 0 , it being a double cover of M − ) under the map J − : (t, x, y, z) → (t, −x, −y, z + a). Our interest in M − , as well as it being an interesting topologically non-trivial spacetime in which we can probe the effect of topology on the Unruh effect, lies in its role in modelling, via accelerated observers on flat spacetimes, the Hawking(-Unruh) effect on the RP 3 geon [9].…”

Section: Scalar Detector On M −mentioning

confidence: 99%

“…In contrast to the analogous result on M with boundary, there is no divergence here at x = 0 as there is no obstruction there and the inertial detector on M − carries through x = 0 smoothly. Note that on M − the energy-momentum tensor expectation values are finite over the whole spacetime [9,31], while on M with boundary they diverge at x = 0. For ω > 0 the M 0 part of the transition rate vanishes while the image part is odd in τ .…”

Section: Inertial Detectormentioning

confidence: 99%

Causal particle detectors and topology

Langlois¹

2006

Annals of Physics

Self Cite

124

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We investigate particle detector responses in some topologically non-trivial spacetimes. We extend a recently proposed regularization of the massless scalar field Wightman function in 4-dimensional Minkowski space to arbitrary dimension, to the massive scalar field, to quotients of Minkowski space under discrete isometry groups and to the massless Dirac field. We investigate in detail the transition rate of inertial and uniformly accelerated detectors on the quotient spaces under groups generated by $(t,x,y,z)\mapsto(t,x,y,z+2a)$, $(t,x,y,z)\mapsto(t,-x,y,z)$, $(t,x,y,z)\mapsto(t,-x,-y,z)$, $(t,x,y,z)\mapsto(t,-x,-y,z+a)$ and some higher dimensional generalizations. For motions in at constant $y$ and $z$ on the latter three spaces the response is time dependent. We also discuss the response of static detectors on the RP^3 geon and inertial detectors on RP^3 de Sitter space via their associated global embedding Minkowski spaces (GEMS). The response on RP^3 de Sitter space, found both directly and in its GEMS, provides support for the validity of applying the GEMS procedure to detector responses and to quotient spaces such as RP^3 de Sitter space and the RP^3 geon where the embedding spaces are Minkowski spaces with suitable identifications.Comment: 47 pages, 9 figure

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Stress tensor for massive fields on flat spaces of spatial topology

Cited by 4 publications

References 15 publications

Mass dependence of quantum energy inequality bounds

Mass dependence of quantum energy inequality bounds

Quantum energy inequalities and local covariance. I. Globally hyperbolic spacetimes

Causal particle detectors and topology

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