172 research outputs found
Existence and properties of p-tupling fixed points
We prove the existence of fixed points of p-tupling renormalization operators
for interval and circle mappings having a critical point of arbitrary real
degree r > 1. Some properties of the resulting maps are studied: analyticity,
univalence, behavior as tends to infinity.Comment: LaTeX 2
Trees
An algebraic formalism, developped with V. Glaser and R. Stora for the study
of the generalized retarded functions of quantum field theory, is used to prove
a factorization theorem which provides a complete description of the
generalized retarded functions associated with any tree graph. Integrating over
the variables associated to internal vertices to obtain the perturbative
generalized retarded functions for interacting fields arising from such graphs
is shown to be possible for a large category of space-times.Comment: minor corrections, references added, no change in result
de Sitter tachyons and related topics
We present a complete study of a family of tachyonic scalar fields living on
the de Sitter universe. We show that for an infinite set of discrete values of
the negative squared mass the fields exhibit a gauge symmetry and there exists
for them a fully acceptable local and covariant quantization similar to the
Feynman-Gupta-Bleuler quantization of free QED. For general negative squares
masses we also construct positive quantization where the de Sitter symmetry is
spontaneously broken. We discuss the sense in which the two quantizations may
be considered physically inequivalent even when there is a Lorentz invariant
subspace in the second one.Comment: Updated reference
Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time
We propose a general framework for quantum field theory on the de Sitter
space-time (i.e. for local field theories whose truncated Wightman functions
are not required to vanish). By requiring that the fields satisfy a weak
spectral condition, formulated in terms of the analytic continuation properties
of their Wightman functions, we show that a geodesical observer will detect in
the corresponding ``vacuum'' a blackbody radiation at temperature T=1/(2 \pi
R). We also prove the analogues of the PCT, Reeh-Schlieder and
Bisognano-Wichmann theorems.Comment: 32 pages, Latex. To appear on Commun. Math. Phy
Scalar tachyons in the de Sitter universe
We provide a construction of a class of local and de Sitter covariant
tachyonic quantum fields which exist for discrete negative values of the
squared mass parameter and which have no Minkowskian counterpart. These quantum
fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly
is a covariant field which can be used to select the physical subspace (of
finite codimension) where the homogeneous tachyonic field equation holds in the
usual form. We show that the model is local and de Sitter invariant on the
physical space. Our construction also sheds new light on the massless minimally
coupled field, which is a special instance of it.Comment: 9 page
Towards a General Theory of Quantized Fields on the Anti-de Sitter Space-Time
We propose a general framework for studying quantum field theory on the
anti-de-Sitter space-time, based on the assumption of positivity of the
spectrum of the possible energy operators. In this framework we show that the
n-point functions are analytic in suitable domains of the complex AdS manifold,
that it is possible to Wick rotate to the Euclidean manifold and come back, and
that it is meaningful to restrict AdS quantum fields to Poincare' branes. We
give also a complete characterization of two-point functions which are the
simplest example of our theory. Finally we prove the existence of the AdS-Unruh
effect for uniformly accelerated observers on trajectories crossing the
boundary of AdS at infinity, while that effect does not exist for all the other
uniformly accelerated trajectories.Comment: LaTex, 43 pages, 2 figures. New introduction. Discussion of the
AdS-Unruh effect expanded. Final section added. To be published on CM
Banana integrals in configuration space
We reconsider the computation of banana integrals at different loops, by
working in the configuration space, in any dimension. We show how the 2-loop
banana integral can be computed directly from the configuration space
representation, without the need to resort to differential equations, and we
include the analytic extension of the diagram in the space of complex masses.
We also determine explicitly the expansion of the two loop banana
integrals, for , .Comment: 29 pages, several formulas improved, removed a mistak
Banana integrals in configuration space
We reconsider the computation of banana integrals at different loops, by working in the configuration
space, in any dimension. We show how the 2-loop banana integral can be computed directly from the
configuration space representation, without the need to resort to differential equations, and we include
the analytic extension of the diagram in the space of complex masses. We also determine explicitly the Δ
expansion of the two loop banana integrals, for d = j â 2Δ, j = 2, 3, 4
Anti de Sitter quantum field theory and a new class of hypergeometric identities
We use Anti-de Sitter quantum field theory to prove a new class of identities
between hypergeometric functions related to the K\"all\'en-Lehmann
representation of products of two Anti-de Sitter two-point functions. A rich
mathematical structure emerges. We apply our results to study the decay of
unstable Anti-de Sitter particles. The total amplitude is in this case finite
and Anti-de Sitter invariant
The maximum principle and sign changing solutions of the hyperbolic equation with the Higgs potential
In this article we discuss the maximum principle for the linear equation and
the sign changing solutions of the semilinear equation with the Higgs
potential. Numerical simulations indicate that the bubbles for the semilinear
Klein-Gordon equation in the de Sitter spacetime are created and apparently
exist for all times
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