共查询到20条相似文献,搜索用时 948 毫秒
1.
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated
in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not
possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require
symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory,
wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field
theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having
to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum
field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot
vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing
vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of
a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.
Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation. 相似文献
2.
We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using
the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model,
we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible
scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally
identified with the physical spacetime. 相似文献
3.
Rodolfo Gambini Jorge Pullin Saeed Rastgoo 《General Relativity and Gravitation》2011,43(12):3569-3592
We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there
are local degrees of freedom one faces the “problem of dynamics”. We attack it using the “uniform discretization technique”.
We find the quantum state that minimizes the value of the master constraint for the case of weak fields and curvatures. The
state has the form of a direct product of Gaussians for the gravitational variables times a modified Fock state for the scalar
field. In this paper we do three things. First, we verify that the previous state also yields a small value of the master
constraint when one polymerizes the scalar field in addition to the gravitational variables. We then study the propagators
for the polymerized scalar field in flat space-time using the previously considered ground state in the low energy limit.
We discuss the issue of the Lorentz invariance of the whole approach. We note that if one uses real clocks to describe the
system, Lorentz invariance violations are small. We discuss the implications of these results in the light of Hořava’s Gravity at the Lifshitz point and of the argument about potential large Lorentz violations in interacting field theories of Collins et al. 相似文献
4.
T. Padmanabhan 《General Relativity and Gravitation》2008,40(2-3):529-564
I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding
the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence
for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a
candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant.
Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain
key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter
fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that
until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant
problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms
of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective
theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the
shift of the matter energy momentum tensor T
ab
→ T
ab
+ Λ
gab
and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed
value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary
of a spacetime region. 相似文献
5.
6.
This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation—as well as conceptual overthrow—of this geometric ether. 相似文献
7.
The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally
well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of
the presence or absence of gravity. In this sense, one can say that the charge “substratum” and the flux “substratum” are
not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized
as the spacetime relation
H = H(F) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F, is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime
relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be
accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to
a violation of the equivalence principle. 相似文献
8.
Rainer Verch 《Communications in Mathematical Physics》2001,223(2):261-288
A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic
spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory
is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates
on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of
a causal dynamical law, fixed spinor- or tensor type for all quantum fields of the theory, and that the quantum field on Minkowski
spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem holds: If for some of the spacetimes
the corresponding quantum field obeys the “wrong” connection between spin and statistics, then all quantum fields of the theory,
on each spacetime, are trivial.
Received: 1 March 2001 / Accepted: 28 May 2001 相似文献
9.
Zhao-Yan Wu 《理论物理通讯》2016,65(6):716-730
Based on a general variational principle, Einstein-Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical objects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining “change of a particle’s energy-momentum”, we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force. 相似文献
10.
In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum
field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting
theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and K?hler, and by Brunetti and
Fredenhagen, but they did not impose any “locality” or “covariance” condition in their constructions. As a consequence, their
construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary
parameters. In this paper, we construct an “extended Wick polynomial algebra”– large enough to contain the Wick polynomials
and their time ordered products – by generalizing a construction of Dütsch and Fredenhagen to curved spacetime. We then
define the notion of a local, covariant quantum field, and seek a definition of local Wick polynomials and their time ordered products as local, covariant quantum fields. We introduce a new notion of the scaling
behavior of a local, covariant quantum field, and impose scaling requirements on our local Wick polynomials and their time
ordered products as well as certain additional requirements – such as commutation relations with the free field and appropriate
continuity properties under variations of the spacetime metric. For a given polynomial order in powers of the field, we prove
that these conditions uniquely determine the local Wick polynomials and their time ordered products up to a finite number
of parameters. (These parameters correspond to the usual renormalization ambiguities occurring in Minkowski spacetime together
with additional parameters corresponding to the coupling of the field to curvature.) We also prove existence of local Wick
polynomials. However, the issue
of existence of local time ordered products is deferred to a future investigation.
Received: 27 March 2001 / Accepted: 6 June 2001 相似文献
11.
A. M. Baranov 《Russian Physics Journal》1995,38(5):503-507
Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995. 相似文献
12.
B. Lamine M.-T. Jaekel S. Reynaud 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,20(2):165-176
We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the
“direct” gravitational effect registered by the phase of the matter waves as well as the “indirect” effect registered by the
light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we
show that both effects are negligible for the presently studied interferometers.
Received 15 February 2002 / Received in final form 12 April 2002 Published online 19 July 2002 相似文献
13.
The physical specificity of gravity as a Goldstone-type field responsible for spontaneous breaking of space-time symmetries
is investigated and extended up to supergravity. Problems of the Higgs gravitation vacuum and its matter sources are discussed.
A particular “dislocation” structure of a space-time due to Poincaré translation gauge fields and the corresponding modification
of Newton’s gravitational potential are predicted. 相似文献
14.
In the bounds of the consistent dynamic interpretation of gravitation (gravidynamics) a gravitational field is divided into
two components: scalar and tensor, each interacting with its sources by the same coupling constant. Generated by a massive
object, a spherically-symmetrical gravitational field in vacuum has an effect on test bodies as an algebraic sum of attraction
(proper gravitation) and repulsion (or antigravitation). The source of the scalar part of the field (or the source of antigravitation)
is the trace of the energy-momentum tensor of the gravitating body, which is determined in the end by the total mass M or the total energy Mc
2 of this body, including its “coat” consisting of virtual gravitons.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
James P. Crawford 《Foundations of Physics》1998,28(3):457-470
A fundamental tenet of general relativity is geodesic motion of point particles. For extended objects, however, tidal forces make the trajectories deviate from geodesic form. In fact Mathisson, Papapetrou, and others have found that even in the limit of very small size there exists a residual curvature-spin force. Another important physical case is that of field theory. Here the ray (WKB) approximation may be used to obtain the equation of motion. In this article I consider an alternative procedure, the proper time translation operator formalism, to obtain the covariant Heisenberg equations for the quantum velocity, momentum, and angular momentum operators for the case of spinor fields. I review the flat spacetime results for Dirac particles in Yang-Mills fields, where we recover the Lorentz force. For curved spacetime I find that the geodesic equation is modified by an additional term involving the spin tensor, and the parallel transport equation for the momentum is modified by an additional term involving the curvature tensor. This curvature term is the Lorentz force of the gravitational field. The main result of this article is that these equations are exactly the (symmetrized) Mathisson-Papapetrou equations for the quantum operators. Extension of these results to the case of spin-one fields may be possible by use of the KDP formalism. 相似文献
16.
Given a multifractal spectrum, we consider the problem of whether it is possible to recover the potential that originates
the spectrum. The affirmative solution of this problem would correspond to a “multifractal” classification of dynamical systems,
i.e., a classification solely based on the information given by multifractal spectra. For the entropy spectrum on topological
Markov chains we show that it is possible to have both multifractal rigidity and multifractal “nonrigidity”, by appropriately
varying the Markov chain and the potential defining the spectrum. The “nonrigidity” even occurs in some generic sense. This
strongly contrasts to the usual opinion among some experts that it should be possible to recover the potential up to some
equivalence relation, at least in some generic sense.
Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, through FCT by Program POCTI/FEDER and
the grant SFRH/BD/10154/2002. 相似文献
17.
Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the “volume integral
quantifier,” which provides a measure of the “total amount” of energy condition violating matter. Secondly, we present a specific
metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that
the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is
constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In
order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby
satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure
across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole,
namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity
of an observer journeying through the wormhole, are also found by imposing the traversability conditions. 相似文献
18.
Donato Bini Christian Cherubini Simonetta Filippi Andrea Geralico 《General Relativity and Gravitation》2009,41(12):2781-2795
An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed
with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild
solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in
this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source
and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s
model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source
and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for
extended bodies in general relativity. 相似文献
19.
A dynamical model for varying light velocity in cosmology is developed, based on the idea that there are two metrics in spacetime. One metric gμν describes the standard gravitational vacuum, and the other
describes the geometry through which matter fields propagate. Matter propagating causally with respect to
can provide acausal contributions to the matter stress-energy tensor in the field equations for gμν, which, as we explicitly demonstrate with perfect fluid and scalar field matter models, provides a mechanism for the solution of the horizon, flatness and magnetic monopole problems in an FRW universe. The field equations also provide a ‘graceful exit' to the inflationary epoch since below an energy scale (related to the mass of ψμ) we recover exactly the standard FRW field equations. 相似文献
20.
X. Waintal J.-L. Pichard 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(1):117-121
For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert
space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When
the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the
case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize
the Golden rule decay of the non interacting states and the enhancement factor of the localization length.
Received: 17 April 1998 / Accepted: 14 May 1998 相似文献