316,798 research outputs found
From euclidean field theory to quantum field theory
In order to construct examples for interacting quantum field theory models,
the methods of euclidean field theory turned out to be powerful tools since
they make use of the techniques of classical statistical mechanics.
Starting from an appropriate set of euclidean n-point functions (Schwinger
distributions), a Wightman theory can be reconstructed by an application of the
famous Osterwalder-Schrader reconstruction theorem. This procedure (Wick
rotation), which relates classical statistical mechanics and quantum field
theory, is, however, somewhat subtle. It relies on the analytic properties of
the euclidean n-point functions.
We shall present here a C*-algebraic version of the Osterwalder-Scharader
reconstruction theorem. We shall see that, via our reconstruction scheme, a
Haag-Kastler net of bounded operators can directly be reconstructed.
Our considerations also include objects, like Wilson loop variables, which
are not point-like localized objects like distributions. This point of view may
also be helpful for constructing gauge theories.Comment: 35 page
Locally covariant quantum field theory with external sources
We provide a detailed analysis of the classical and quantized theory of a
multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime
metric and also to an external source term; thus the solutions form an affine
space. Following the formulation of affine field theories in terms of
presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171
(2014)], we determine the relative Cauchy evolution induced by metric as well
as source term perturbations and compute the automorphism group of natural
isomorphisms of the presymplectic vector space functor. Two pathological
features of this formulation are revealed: the automorphism group contains
elements that cannot be interpreted as global gauge transformations of the
theory; moreover, the presymplectic formulation does not respect a natural
requirement on composition of subsystems. We therefore propose a systematic
strategy to improve the original description of affine field theories at the
classical and quantized level, first passing to a Poisson algebra description
in the classical case. The idea is to consider state spaces on the classical
and quantum algebras suggested by the physics of the theory (in the classical
case, we use the affine solution space). The state spaces are not separating
for the algebras, indicating a redundancy in the description. Removing this
redundancy by a quotient, a functorial theory is obtained that is free of the
above mentioned pathologies. These techniques are applicable to general affine
field theories and Abelian gauge theories. The resulting quantized theory is
shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references
added. v3: 47 pages; compatible with version to appear in Annales Henri
Poincar
D-brane effective field theory from string field theory
Open string field theory is considered as a tool for deriving the effective
action for the massless or tachyonic fields living on D-branes. Some simple
calculations are performed in open bosonic string field theory which validate
this approach. The level truncation method is used to calculate successive
approximations to the quartic terms \phi^4, (A^\mu A_\mu)^2 and [A_\mu,
A_\nu]^2 for the zero momentum tachyon and gauge field on one or many bosonic
D-branes. We find that the level truncation method converges for these terms
within 2-4% when all massive fields up to level 20 are integrated out, although
the convergence is slower than exponential. We discuss the possibility of
extending this work to determine the structure of the nonabelian Born-Infeld
theory describing the gauge field on a system of many parallel bosonic or
supersymmetric D-branes. We also describe a brane configuration in which
tachyon condensation arises in both the gauge theory and string field theory
pictures. This provides a natural connection between recent work of Sen and
Zwiebach on tachyon condensation in string field theory and unstable vacua in
super Yang-Mills and Born-Infeld field theory.Comment: 23 pages, 4 figures, LaTeX; v3: sign error corrected, references
added, discussion of bosonic NBI extended. v4: bug in N coefficient table
fixed; qualitative results unchange
Euclidean Field Theory
A coincise review about Euclidean (Quantum) Field Theory is presented. It
deals with the general structural properties, the connections with Quantum
Field Theory, the exploitation in Constructive Quantum Field Theory, and the
physical interpretation.Comment: 19 page
Noncommutative Field Theory
We review the generalization of field theory to space-time with noncommuting
coordinates, starting with the basics and covering most of the active
directions of research. Such theories are now known to emerge from limits of M
theory and string theory, and to describe quantum Hall states. In the last few
years they have been studied intensively, and many qualitatively new phenomena
have been discovered, both on the classical and quantum level.
To appear in Reviews of Modern Physics.Comment: Revtex, 56 pp, 6 figures. Final versio
Information field theory
Non-linear image reconstruction and signal analysis deal with complex inverse
problems. To tackle such problems in a systematic way, I present information
field theory (IFT) as a means of Bayesian, data based inference on spatially
distributed signal fields. IFT is a statistical field theory, which permits the
construction of optimal signal recovery algorithms even for non-linear and
non-Gaussian signal inference problems. IFT algorithms exploit spatial
correlations of the signal fields and benefit from techniques developed to
investigate quantum and statistical field theories, such as Feynman diagrams,
re-normalisation calculations, and thermodynamic potentials. The theory can be
used in many areas, and applications in cosmology and numerics are presented.Comment: 8 pages, in-a-nutshell introduction to information field theory (see
http://www.mpa-garching.mpg.de/ift), accepted for the proceedings of MaxEnt
2012, the 32nd International Workshop on Bayesian Inference and Maximum
Entropy Methods in Science and Engineerin
Quantum Field Theory
I discuss the general principles underlying quantum field theory, and attempt
to identify its most profound consequences. The deepest of these consequences
result from the infinite number of degrees of freedom invoked to implement
locality. I mention a few of its most striking successes, both achieved and
prospective. Possible limitations of quantum field theory are viewed in the
light of its history.Comment: LaTeX, 12 pages, 3 figures. Will appear in Centenary issue of Rev. of
Mod. Phys., March 1999. Incorporated minor corrections suggested by edito
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