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1.
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance
and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation
of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated
in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework
for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status,
and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for
the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum
field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such
as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the
coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved
spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of
our new viewpoint on quantum field theory are discussed. 相似文献
2.
We present an algorithm for constructing the Wilson operator product expansion (OPE) for perturbative interacting quantum
field theory in general Lorentzian curved spacetimes, to arbitrary orders in perturbation theory. The remainder in this expansion
is shown to go to zero at short distances in the sense of expectation values in arbitrary Hadamard states. We also establish
a number of general properties of the OPE coefficients: (a) they only depend (locally and covariantly) upon the spacetime
metric and coupling constants, (b) they satisfy an associativity property, (c) they satisfy a renormalization group equation,
(d) they satisfy a certain microlocal wave front set condition, (e) they possess a “scaling expansion”. The latter means that
each OPE coefficient can be written as a sum of terms, each of which is the product of a curvature polynomial at a spacetime
point, times a Lorentz invariant Minkowski distribution in the tangent space of that point. The algorithm is illustrated in
an example. 相似文献
3.
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
4.
Rainer Verch 《Communications in Mathematical Physics》1999,205(2):337-367
The investigation of wavefront sets of n-point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the
help of concepts from microlocal analysis in quantum field theory in curved spacetime. In the present paper, the notion of
wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator
algebras carrying a covariant action of the translation group in arbitrary dimension. In the case where one is given a quantum
field theory in the operator algebraic framework, this generalized notion of wavefront set, called “asymptotic correlation
spectrum”, is further investigated and several of its properties for physical states are derived. We also investigate the
connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding Wightman
distributions if there is a Wightman field
affiliated to the local operator algebras. Finally we present a new result (generalizing known facts) which shows that certain
spacetime points must be contained in the singular supports of the 2n-point distributions of a non-trivial Wightman field.
Received: 27 July 1998 / Accepted: 3 March 1999 相似文献
5.
Robert Oeckl 《Czechoslovak Journal of Physics》2001,51(12):1401-1406
The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum
group symmetries, one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most attention
has so far been focused on the case with maximal symmetry — where the base space is a quantum group and the bimodules are
bicovariant. The structure of bicovariant bimodules is well understood through their correspondence with crossed modules.
We investigate the “next best” case — where the base space is a quantum homogeneous space and the bimodules are covariant.
We present a structure theorem that resembles the one for bicovariant bimodules. Thus, there is a correspondence between covariant
bimodules and a new kind of “crossed” modules which we define. The latter are attached to the pair of quantum groups which
defines the quantum homogeneous space.
We apply our structure theorem to differential calculi on quantum homogeneous spaces and discuss a related notion of induced
differential calculus.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
This work was supported by a NATO fellowship grant. 相似文献
6.
S. Carlip 《International Journal of Theoretical Physics》2007,46(9):2192-2203
Black hole entropy appears to be “universal”—many independent calculations, involving models with very different microscopic
degrees of freedom, all yield the same density of states. I discuss the proposal that this universality comes from the behavior
of the underlying symmetries of the classical theory. To impose the condition that a black hole be present, we must partially
break the classical symmetries of general relativity, and the resulting Goldstone-boson-like degrees of freedom may account
for the Bekenstein–Hawking entropy. In particular, I demonstrate that the imposition of a “stretched horizon” constraint modifies
the algebra of symmetries at the horizon, allowing the use of standard conformal field theory techniques to determine the
asymptotic density of states. The results reproduce the Bekenstein–Hawking entropy without any need for detailed assumptions
about the microscopic theory. 相似文献
7.
P.H. Chankowski S. Pokorski J. Wagner 《The European Physical Journal C - Particles and Fields》2007,50(4):919-933
We consider the electroweak theory with an additional Higgs triplet at one loop, using the hybrid renormalization scheme based
on αEM, GF and MZ as input observables. We show that in this scheme loop corrections can in a natural way be split into a standard model part
and corrections due to “new physics”. The latter, however, do not decouple in the limit of an infinite triplet mass parameter,
if the triplet trilinear coupling to the SM Higgs doublets grows with the triplet mass. For electroweak observables computed
at one loop this effect can be attributed to the radiative generation in this limit of a nonvanishing vacuum expectation value
of the triplet. We also point out that whenever tree level expressions for the electroweak observables depend on vacuum expectation
values of scalar fields other than the standard model Higgs doublet, a tadpole contribution to the “oblique” parameter T should
in principle be included. The origin of nondecoupling is discussed also on the basis of symmetry principles in a simple scalar
field theory. 相似文献
8.
A. A. Kirillov 《Journal of Experimental and Theoretical Physics》1999,88(6):1051-1057
It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields
is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed,
and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related
to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can
be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density.
From the effective-field standpoint, such particles are “dark.” It is assumed that they comprise dark matter of the universe.
The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field
potentials.
Zh. éksp. Teor. Fiz. 115, 1921–1934 (June 1999) 相似文献
9.
We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Frölicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position representations in curved spacetime, in terms of generalized semi-densities, leads to a definition of quantum configuration bundle which is suitable for a treatment of that kind. A consistent approach to Lagrangian field theories, vertical infinitesimal symmetries and related currents is then developed, and applied to a formulation of BRST symmetry in a gauge theory of the Yang–Mills type. 相似文献
10.
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
11.
Philippe Droz-Vincent 《International Journal of Theoretical Physics》2009,48(7):2177-2189
We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external
field, when this field is “strongly” translation invariant in some directions and additionally remains unchanged by other
isometries of spacetime. Since the relativistic interactions cannot be composed additively, it is not a priori garanteed that the two-body system inherits all the symmetries of the external potential. However, using an ansatz which
permits to preserve the compatibility of the mass-shell constraints in the presence of the field, we show how the “surviving
isometries” can actually be implemented in the two-body wave equations. 相似文献
13.
Rafael D. Sorkin 《International Journal of Theoretical Physics》1997,36(12):2759-2781
In seeking to arrive at a theory of “quantum gravity,” one faces several choices among alternative approaches. I list some
of these “forks in the road” and offer reasons for taking one alternative over the other. In particular, I advocate the following:
the sum-over-histories framework for quantum dynamics over the “observable and state-vector” framework; relative probabilities
over absolute ones; spacetime over space as the gravitational “substance” (4 over 3+1); a Lorentzian metric over a Riemannian
(“Euclidean”) one; a dynamical topology over an absolute one; degenerate metrics over closed timelike curves to mediate topology
change; “unimodular gravity” over the unrestricted functional integral; and taking a discrete underlying structure (the causal
set) rather than the differentiable manifold as the basis of the theory. In connection with these choices, I also mention
some results from unimodular quantum cosmology, sketch an account of the origin of black hole entropy, summarize an argument
that the quantum mechanical measurement scheme breaks down for quantum field theory, and offer a reason why the cosmological
constant of the present epoch might have a magnitude of around 10−120 in natural units.
This paper is the text of a talk given at the symposium on Directions in General Relativity held at the University of Maryland,
College Park, Maryland, in May 1993 in honor of Dieter Brill and Charles Minser. 相似文献
14.
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
15.
Roberto Longo 《Communications in Mathematical Physics》2001,222(1):45-96
We view DHR superselection sectors with finite statistics as Quantum Field Theory analogs of elliptic operators where KMS
functionals play the role of the trace composed with the heat kernel regularization. We extend our local holomorphic dimension
formula and prove an analogue of the index theorem in the Quantum Field Theory context. The analytic index is the Jones index,
more precisely the minimal dimension, and, on a 4-dimensional spacetime, the DHR theorem gives the integrality of the index.
We introduce the notion of holomorphic dimension; the geometric dimension is then defined as the part of the holomorphic dimension
which is symmetric under charge conjugation. We apply the AHKT theory of chemical potential and we extend it to the low dimensional
case, by using conformal field theory. Concerning Quantum Field Theory on a curved spacetime, the geometry of the manifold
enters in the expression for the dimension. If a quantum black hole is described by a spacetime with bifurcate Killing horizon
and
sectors are localizable on the horizon, the variation of logarithm of the geometric dimension is proportional to the incremental
free energy, due to the addition of the charge, and to the inverse temperature, hence to the inverse of the surface gravity
in the Hartle–Hawking KMS state. For this analysis we consider a conformal net obtained by restricting the field to the horizon
(“holography”). Compared with our previous work on Rindler spacetime, this result differs inasmuch as it concerns true black
hole spacetimes, like the Schwarzschild–Kruskal manifold, and pertains to the entropy of the black hole itself, rather than
of the outside system. An outlook concerns a possible relation with supersymmetry and noncommutative geometry.
Received: 8 March 2000 / Accepted: 17 April 2001 相似文献
16.
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
17.
18.
P. Leifer 《Foundations of Physics》1997,27(2):261-285
The ordinary quantum theory points out that general relativity (GR) is negligible for spatial distances up to the Planck scale
lP=(hG/c3)1/2∼10−33cm. Consistency in the foundations of the quantum theory requires a “soft” spacetime structure of the GR at essentially longer
length. However, for some reasons this appears to be not enough. A new framework (“superrelativity”) for the desirable generalization
of the foundation of quantum theory is proposed. A generalized nonlinear Klein-Gordon equation has been derived in order to
shape a stable wave packet. 相似文献
19.
Tevian Dray Ravi Kulkarni Corinne A. Manogue 《General Relativity and Gravitation》1992,24(12):1255-1266
A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces.
The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure
for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads
to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial
Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside
the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in”
and “out” Boulware vacua. 相似文献