This dissertation presents a semiclassical analysis of conical topology change in $1+1$ spacetime dimensions wherein, to lowest order, the ambient spacetime is classical and fixed while the scalar field coupled to it is quantized. The vacuum expectation value of the scalar field stress-energy tensor is calculated via two different approaches. The first of these involves the explicit determination of the so called Sorkin-Johnston state on the cone and an original regularization scheme, while the latter employs the conformal vacuum and the more conventional point-splitting renormalization. It is found that conical topology change seems not to suffer from the same pathologies that trousers-type topology change does. This provides tentative agreement with conjectures due to Sorkin and Borde, which attempt to classify topology changing spacetimes with respect to their Morse critical points and in particular, that the cone and yarmulke in $1+1$ dimensions lack critical points of unit Morse index.
Vacuum structure and global cosmic strings are analyzed in the effective theory of self-interacting O(2) scalar fields on (3+1)-manifolds with conical singularities. In the context of one-loop effective action computed by heat-kernel methods with $ζ$-function regularization, we find an inhomogeneous vacuum of minimum energy and suggest some reason why low-energy global strings are likely to be generated at the conical singularities.
We consider a quasi-periodically identified conical spacetime, like the one of a cosmic string or disclination, to investigate nonzero averaged quantum vacuum fluctuations effects on the energy-momentum tensor and induced current density associated with a charged scalar field. We obtain exactly closed analytical expressions for the two-point Wightman function and the vacuum expectation value of the field squared, as well as for all components of the energy-momentum tensor. As to the induced current density, due to the quasi-periodic condition used, the only nonzero averaged component found is …
We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a three-brane and two-dimensional conical space transverse to the latter. In addition, we assume the presence of an extra magnetic flux along the core of the conical space. The heat kernel and the Feynman Green function are presented in the form of a sum of two terms. The first one corresponds to the contribution coming from the bulk with global monopole in the abs…
A previously introduced method to renormalize the one-loop stress tensor and the one-loop vacuum fluctuations in a curved background by a direct local $ζ$-function approach is checked in some thermal and nonthermal cases. First the method is checked in the case of a conformally coupled massless field in the static Einstein universe where all hypotheses initially requested by the method hold true. Secondly, dropping the hypothesis of a closed manifold, the method is checked in the open static Einstein universe. Finally, the method is checked for a massless scalar field in the presence of a coni…
Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit form of the matching conditions depends on the field under consideration. In the case of electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions ($δ$-potential) on the cylindrical shell are investigated. As a res…
Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In the…
We study the fluctuations of the stress tensor for a massless scalar field in two and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of derivatives of a scalar function. These expressions allow one to express spacetime averages of the correlation function as finite integrals. We also study the correlation between measurements of the energy density along a worldline. We find that these measurements may be either positively correlated or anticorrelated. The anticorrelated measurements can be interpre…
We analyze the quantum fluctuations of vacuum stress tensors and spacetime curvatures, using the framework of linear response theory which connects these fluctuations to dissipation mechanisms arising when stress tensors and spacetime metric are coupled. Vacuum fluctuations of spacetime curvatures are shown to be a sum of two contributions at lowest orders; the first one corresponds to vacuum gravitational waves and is restricted to light-like wavevectors and vanishing Einstein curvature, while the second one arises from gravity of vacuum stress tensors. From these fluctuations, we deduce nois…
We consider vacuum polarization effect of a conformally coupled massless scalar field in the background produced by an idealized straight cosmic string. Using previous criterion we show the calculation of back reaction of the field to the metric in the context of semiclassical gravity theory is not valid , in some regions due to large quantum fluctuations in the conical space.
We revisit two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. Appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.
In the context of Born-Infeld \emph{determinantal} gravity formulated in a n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional \emph{vacuum} circular symmetric solution without cosmological constant consisting in a rotating spacetime with non singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is c…
We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement process for a stress tensor component, such as the energy density of a quantized field in its vacuum state. Although spatial averaging reduces the probability of large vacuum fluctuations compared to time averaging alone, we find that the probability distribution decreases more slowly than exponentially as the magnitude of the measured energy density increa…
Representations of the Klein-Gordon and Dirac propagators are determined in a $N$ dimensional conical background for massive fields twisted by an arbitrary angle $2πσ$. The Dirac propagator is shown to be obtained from the Klein-Gordon propagator twisted by angles $2πσ\pm {\cal D}/2$ where ${\cal D}$ is the cone deficit angle. Vacuum expectation values are determined by a point-splitting method in the proper time representation of the propagators. Analogies with the Aharonov-Bohm effect are pointed out throughout the paper and a conjecture on an extension to fields of arbitrary spin is given.
We explore the new technique developed recently in \cite{Rosenhaus:2014woa} 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 sp…
Vacuum polarization and renormalized stress-energy tensor of spherical thin shells
SISSA, International School for Advanced Studies（国际高等研究院）；INFN Sezione di Trieste（的里雅斯特INFN分部）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Technological University Dublin（都柏林科技大学）；University College Dublin（都柏林大学学院）；Dublin City University（都柏林城市大学）
We found the contribution to the vacuum expectation value of the energy-momentum tensor of a massive Dirac field due to the conical geometry of the cosmic string space-time. The heat kernel and heat kernel expansion for the squared Dirac operator in this background are also considered and the first three coefficients were found in an explicity form.
We apply recent results on the probability distribution for quantum stress tensor fluctuations to the problem of barrier penetration by quantum particles. The probability for large stress tensor fluctuations decreases relatively slowly with increasing magnitude of the fluctuation, especially when the quantum stress tensor operator has been averaged over a finite time interval. This can lead to large vacuum radiation pressure fluctuations on charged or polarizable particles, which can in turn push the particle over a potential barrier. The rate for this effect depends sensitively upon the detai…
We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuu…
Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008, gr-qc/9604009], I investigate the various point-wise and averaged energy conditions in the Unruh vacuum. I consider the quantum stress-energy tensor corresponding to a conformally coupled massless scalar field, work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. I construct a semi-analytic model for the stress-energy tensor that globally reproduces all known numerical results to within 0.8%, and satisfies all known analytic features of t…
We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.
A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process. Realistic measurements can be expected to begin and end at finite times, which means that they are described by functions with compact support, which we will also take to be smooth. Here we study the probability distributions for stress tensor operators averaged with such functions of time, in the vacuum state of a massless free field. Our primary aim is to…
We present the solution of the problem of the $1/\Box, \Box \to 0,$ asymptotic terms discovered in the one-loop form factors of the gravitational effective action. Owing to certain constraints among their coefficients, which we establish, these terms cancel in the vacuum stress tensor and do not violate the asymptotic flatness of the expectation value of the metric. They reappear, however, in the Riemann tensor of this metric and stand for a new effect: a radiation of gravitational waves induced by the vacuum stress. This coherent radiation caused by the backreaction adds to the noncoherent ra…
The Unruh effect has been investigated from the point of view of the quantum statistical Zubarev density operator in space with the Minkowski metric. Quantum corrections of the fourth order in acceleration to the energy-momentum tensor of real and complex scalar fields, and Dirac field are calculated. Both massless and massive fields are considered. The method for regularization of discovered infrared divergences for scalar fields is proposed. The calculated corrections make it possible to substantiate the Unruh effect from the point of view of the statistical approach, and to explicitly show …
The stress-energy tensor of the quantum vacuum is studied for the particular case of quantum electrodynamics (QED), that is a fictituous universe where only the electromagnetic and the electron-positron fields exist. The integrals involved are ultraviolet divergent but it is suggested that a natural cut-off may exist. It is shown that, in spite of the fact that the stress-energy tensor of the electromagnetic field alone is traceless (i.e the pressure P equals 1/3 the energy density u), the total QED tensor is proportional to the metric tensor to a good approximation (i. e. P = -u). It is propo…
We propose a suitable vacuum state for a quantized Dirac field interacting with a classical scalar field in a Friedman-Robertson-Walker-Lemaitre spacetime. This state is constructed from an extended version of the adiabatic expansion of the associated Fourier modes of the field. We compute the full renormalized stress-energy tensor. For any given initial time, this instantaneous vacuum can always be chosen to have vanishing Fourier modes for the renormalized stress-energy tensor. We check the consistency of the solution for several inflationary models.
We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted Gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value …
The two-point function characterizing the stress tensor fluctuations of a massless minimally coupled field for an invariant vacuum state in de Sitter spacetime is discussed. This two-point function is explicitly computed for spacelike separated points which are geodesically connected. We show that these fluctuations are as important as the expectation value of the stress tensor itself. These quantum field fluctuations will induce fluctuations in the geometry of de Sitter spacetime. This paper is a first step towards the computation of such metric fluctuations, which may be of interest for larg…
The renormalized energy-momentum tensor of vacuum has been deeply explored many years ago. The main result of these studies was that such a tensor should satisfy the conservation laws which reflects the covariance of the theory in the presence of loop corrections. In view of this general result we address two important questions, namely how to implement the momentum cut-off in a covariant way and whether this general result holds in the theory with Spontaneous Symmetry Breaking. In the last case some new interesting details arise and although the calculations are more involved we show that the…
We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that when the field is in this state, the expectation value of the energy-momentum stress tensor measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Haw…
The form of the vacuum stress-tensor for the quantized scalar field at a dielectric to vacuum interface is studied. The dielectric is modeled to have an index of refraction that varies with frequency. We find that the stress-tensor components, derived from the mode function expansion of the Wightman function, are naturally regularized by the reflection and transmission coefficients of the mode at the boundary. Additionally, the divergence of the vacuum energy associated with a perfectly reflecting mirror is found to disappear for the dielectric mirror at the expense of introducing a new energy…
We construct a new set of asymptotically flat, static vacuum solutions to the Einstein equations in dimensions 4 and 5, which may be interpreted as a superposition of positive and negative mass black holes. The resulting spacetimes are axisymmetric in 4-dimensions and bi-axisymmetric in 5-dimensions, and are regular away from the negative mass singularities, for instance conical singularities are absent along the axes. In 5-dimensions, the topologies of signed mass black holes used in the construction may be either spheres $S^3$ or rings $S^1 \times S^2$; in particular, the negative mass stati…
We consider the relative entropy between the vacuum state and a state obtained by applying an exponentiated stress tensor to the vacuum of a chiral conformal field theory on the lightray. The smearing function of the stress tensor can be viewed as a vector field on the real line generating a diffeomorphism. We show that the relative entropy is equal to $c$ times the so-called Schwarzian action of the diffeomorphism. As an application of this result, we obtain a formula for the relative entropy between the vacuum and a solitonic state.
In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $ϕ$ with respect to the radius $r$ vanish. If the parameter $α_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2α_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The coni…
It is known that the unregularized expressions for the stress-energy tensor components corresponding to subhorizon and superhorizon vacuum fluctuations of a massless scalar field in a Friedmann-Robertson-Walker background are characterized by the equation of state parameters w=1/3 and w=-1/3, which are not sufficient to produce cosmological acceleration. However, the form of the adiabatically regularized finite stress-energy tensor turns out to be completely different. By using the fact that vacuum subhorizon modes evolve nearly adiabatically and superhorizon modes have w=-1/3, we approximatel…
Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the back-reaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. It will be shown that in the case of general spherically symmetric black holes that have a \emph{dynamical horizon}, as occurs in a cosmological context, one cannot have pair creation on …
A new five dimensional spherical vacuum solution is both dervied and its signature, curvature and truncation discussed. Its truncation leads to a four dimensional spacetime with similiar stress to those found by charge-free Kaluza-Klein compactification. Various other restrictions to four dimensions are looked at to see if they have stresses consisting of electromagnetic fields or quadratic tensors. The solution is extended to the brane picture where the extended space is found to obey field equations with metric stress derivable from a lagrangian dependent on brane function and kaluza scalar.
We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometro-dynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the…
We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge leading to the presence of a finite self-force on the charge from the direction of the point mass exactly as if the point mass itself were charged. The conical space-time geometry also affects the zero point fluctuations of a quantum scalar field leading to the existence of a vacuum polarisation --- $\langle T_\mn \rangle$, in the 2+1 dimensional analog of …
The actual value of the quantum vacuum energy density is generally regarded as irrelevant in non-gravitational physics. However, this paper gives a non-gravitational system where this value does have physical significance. The system is a mirror with an internal degree of freedom which interacts with a scalar field. We find that the force exerted on the mirror by the field vacuum undergoes wild fluctuations with a magnitude proportional to the value of the vacuum energy density, which is mathematically infinite. This infinite fluctuating force gives infinite instantaneous acceleration of the m…
This is a review of recent work on quantum fluctuations of the electric field and of stress tensor operators and their physical effects. The probability distribution for vacuum fluctuations of the electric field is Gaussian, but that for quadratic operators, such as the energy density, can have a more slowly decreasing tail, leading to an enhanced probability of large fluctuations. This effect is very sensitive to the details of how the measurement is performed. Some possible physical effects of these large fluctuations will be discussed.
We compute the leading order contribution to the stress-energy tensor corresponding to the modes of a quantum scalar field propagating in a Friedmann-Robertson-Walker universe with arbitrary coupling to the scalar curvature, whose exact mode functions can be expanded as an infinite adiabatic series. While for a massive field this is a good approximation for all modes when the mass of the field m is larger than the Hubble parameter H, for a massless field only the subhorizon modes with comoving wave-numbers larger than some fixed k* obeying k*/a>H can be analyzed in this way. As infinities comi…
A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy …
Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (…
This paper is devoted to the construction of the renormalized quantum stress energy tensor $\left<T_μ^ν\right>_{ren}$ for a massive scalar field with arbitrary coupling to the gravitational field of a pointlike global monopole, using the Schwinger-DeWitt approximation, up to second order in the inverse mass $μ$ of the field. The given stress energy tensor is constructed by functional differentiation with respect to the metric tensor of the one-loop effective action of sufficiently massive scalar field, such that the Compton length of the quantum field is much less than the characteristic radiu…
We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a ($d+1$)-dimensional flat space-time with topology ${\cal R}\times {\cal S}^d$. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized va…
Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds
Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Institut für Theoretische Physik（理论物理研究所）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息研究中心）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究系宇宙早期研究センター(RESCEU)）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学前沿研究机构 Kavli宇宙物理数学研究所(WPI)）
We propose a method for calculating vacuum fluctuations on the background of a spherical impulsive gravitational wave which results in a finite expression for the vacuum expectation value of the stress-energy tensor. The method is based on first including a cosmological constant as an auxiliary constant. We show that the result for the vacuum expectation value of the stress-energy tensor in second-order perturbation theory is finite if both the cosmological constant and the infrared parameter tend to zero at the same rate.
The Casimir stress on two parallel plates in a de Sitter background corresponding to different metric signatures and cosmological constants is calculated for massless scalar fields satisfying Robin boundary conditions on the plates. Our calculation shows that for the parallel plates with false vacuum between and true vacuum outside, the total Casimir pressure leads to an attraction of the plates at very early universe.
We calculate the expectation value of the coincident product of two field strength tensors at two loop order in scalar electrodynamics on de Sitter background. The result agrees with the stochastic formulation which we have developed in a companion paper [2] for the nonperturbative resummation of leading logarithms of the scale factor. When combined with a previous computation of scalar bilinears [1], our current result also gives the two loop stress-energy tensor for inflationary scalar electrodynamics. This shows a secular decrease in the vacuum energy which derives from the vacuum polarizat…
