353 research outputs found
Transition amplitudes and sewing properties for bosons on the Riemann sphere
We consider scalar quantum fields on the sphere, both massive and massless.
In the massive case we show that the correlation functions define amplitudes
which are trace class operators between tensor products of a fixed Hilbert
space. We also establish certain sewing properties between these operators. In
the massless case we consider exponential fields and have a conformal field
theory. In this case the amplitudes are only bilinear forms but still we
establish sewing properties. Our results are obtained in a functional integral
framework.Comment: 33 page
On Renormalization Group Flows and Polymer Algebras
In this talk methods for a rigorous control of the renormalization group (RG)
flow of field theories are discussed. The RG equations involve the flow of an
infinite number of local partition functions. By the method of exact
beta-function the RG equations are reduced to flow equations of a finite number
of coupling constants. Generating functions of Greens functions are expressed
by polymer activities. Polymer activities are useful for solving the large
volume and large field problem in field theory. The RG flow of the polymer
activities is studied by the introduction of polymer algebras. The definition
of products and recursive functions replaces cluster expansion techniques.
Norms of these products and recursive functions are basic tools and simplify a
RG analysis for field theories. The methods will be discussed at examples of
the -model, the -model and hierarchical scalar field
theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference
``Constructive Results in Field Theory, Statistical Mechanics and Condensed
Matter Physics'', 25-27 July 1994, Palaiseau, Franc
Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes
The mathematical formalism for linear quantum field theory on curved
spacetime depends in an essential way on the assumption of global
hyperbolicity. Physically, what lie at the foundation of any formalism for
quantization in curved spacetime are the canonical commutation relations,
imposed on the field operators evaluated at a global Cauchy surface. In the
algebraic formulation of linear quantum field theory, the canonical commutation
relations are restated in terms of a well-defined symplectic structure on the
space of smooth solutions, and the local field algebra is constructed as the
Weyl algebra associated to this symplectic vector space. When spacetime is not
globally hyperbolic, e.g. when it contains naked singularities or closed
timelike curves, a global Cauchy surface does not exist, and there is no
obvious way to formulate the canonical commutation relations, hence no obvious
way to construct the field algebra. In a paper submitted elsewhere, we report
on a generalization of the algebraic framework for quantum field theory to
arbitrary topological spaces which do not necessarily have a spacetime metric
defined on them at the outset. Taking this generalization as a starting point,
in this paper we give a prescription for constructing the field algebra of a
(massless or massive) Klein-Gordon field on an arbitrary background spacetime.
When spacetime is globally hyperbolic, the theory defined by our construction
coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4
AdS/CFT correspondence in the Euclidean context
We study two possible prescriptions for AdS/CFT correspondence by means of
functional integrals. The considerations are non-perturbative and reveal
certain divergencies which turn out to be harmless, in the sense that
reflection-positivity and conformal invariance are not destroyed.Comment: 20 pages, references and two remarks adde
Local covariant quantum field theory over spectral geometries
A framework which combines ideas from Connes' noncommutative geometry, or
spectral geometry, with recent ideas on generally covariant quantum field
theory, is proposed in the present work. A certain type of spectral geometries
modelling (possibly noncommutative) globally hyperbolic spacetimes is
introduced in terms of so-called globally hyperbolic spectral triples. The
concept is further generalized to a category of globally hyperbolic spectral
geometries whose morphisms describe the generalization of isometric embeddings.
Then a local generally covariant quantum field theory is introduced as a
covariant functor between such a category of globally hyperbolic spectral
geometries and the category of involutive algebras (or *-algebras). Thus, a
local covariant quantum field theory over spectral geometries assigns quantum
fields not just to a single noncommutative geometry (or noncommutative
spacetime), but simultaneously to ``all'' spectral geometries, while respecting
the covariance principle demanding that quantum field theories over isomorphic
spectral geometries should also be isomorphic. It is suggested that in a
quantum theory of gravity a particular class of globally hyperbolic spectral
geometries is selected through a dynamical coupling of geometry and matter
compatible with the covariance principle.Comment: 21 pages, 2 figure
Quantum Field Theory: Where We Are
We comment on the present status, the concepts and their limitations, and the
successes and open problems of the various approaches to a relativistic quantum
theory of elementary particles, with a hindsight to questions concerning
quantum gravity and string theory.Comment: To appear in: An Assessment of Current Paradigms in the Physics of
Fundamental Phenomena, to be published by Springer Verlag (2006
Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment
In this paper, we study inverse scattering of massless Dirac fields that
propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a
stationary approach we determine precisely the leading terms of the high-energy
asymptotic expansion of the scattering matrix that, in turn, permit us to
recover uniquely the mass of the black hole and its charge up to a sign
A geometrical origin for the covariant entropy bound
Causal diamond-shaped subsets of space-time are naturally associated with
operator algebras in quantum field theory, and they are also related to the
Bousso covariant entropy bound. In this work we argue that the net of these
causal sets to which are assigned the local operator algebras of quantum
theories should be taken to be non orthomodular if there is some lowest scale
for the description of space-time as a manifold. This geometry can be related
to a reduction in the degrees of freedom of the holographic type under certain
natural conditions for the local algebras. A non orthomodular net of causal
sets that implements the cutoff in a covariant manner is constructed. It gives
an explanation, in a simple example, of the non positive expansion condition
for light-sheet selection in the covariant entropy bound. It also suggests a
different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio
On the Particle Definition in the presence of Black Holes
A canonical particle definition via the diagonalisation of the Hamiltonian
for a quantum field theory in specific curved space-times is presented. Within
the provided approach radial ingoing or outgoing Minkowski particles do not
exist. An application of this formalism to the Rindler metric recovers the
well-known Unruh effect. For the situation of a black hole the Hamiltonian
splits up into two independent parts accounting for the interior and the
exterior domain, respectively. It turns out that a reasonable particle
definition may be accomplished for the outside region only. The Hamiltonian of
the field inside the black hole is unbounded from above and below and hence
possesses no ground state. The corresponding equation of motion displays a
linear global instability. Possible consequences of this instability are
discussed and its relations to the sonic analogues of black holes are
addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.Comment: 44 pages, LaTeX, no figures, accepted for publication in Phys. Rev.
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