79 research outputs found
An Axiomatic Approach to Semiclassical Perturbative Gauge Field Theories
Different approaches to axionatic field theory are investigated. The main
notions of semiclassical theory are the following: semiclassical states,
Poincare transformations, semiclassical action form, semiclassical gauge
equivalence and semiclassical field. If the manifestly covariant approach is
used, the notion of semiclassical state is related to Schwinger sourse, while
the semicalssical action is presented via the R-function of Lehmann, Symanzik
and Zimmermann. Semiclassical perturbation theory is constructed. Its relation
with the S-matrix theory is investigated. Semiclassical electrodynamics and
non-Abelian gauge theories are studied, making us of the Gupta-Bleuler and BRST
approaches.Comment: 54 page
An Axiomatic Approach to Semiclassical Field Perturbation Theory
Semiclassical perturbation theory is investigated within the framework of
axiomatic field theory. Axioms of perturbation semiclassical theory are
formulated. Their correspondence with LSZ approach and Schwinger source theory
is studied. Semiclassical S-matrix, as well as examples of decay processes, are
considered in this framework.Comment: 32 pages, LaTeX, margins are corrected due to problems with viewing
the PostScript fil
Large-N Theory from the Axiomatic Point of View
The state space and observables for the leading order of the large-N theory
are constructed. The obtained model ("theory of infinite number of fields") is
shown to obey Wightman-type axioms (including invariance under boost
transformations) and to be nontrivial (there are scattering processes, bound
states, unstable particles etc). The considered class of exactly solvable
relativistic quantum models involves good examples of theories containing such
difficulties as volume divergences associated with the Haag theorem,
Stueckelberg divergences and infinite renormalization of the wave function.Comment: 46 pages, LaTe
Exactly Solvable Quantum Mechanical Models with Infinite Renormalization of the Wave Function
The main difficulty of quantum field theory is the problem of divergences and
renormalization. However, realistic models of quantum field theory are
renormalized within the perturbative framework only. It is important to
investigate renormalization beyond perturbation theory. However, known models
of constructive field theory do not contain such difficulties as infinite
renormalization of the wave function. In this paper an exactly solvable quantum
mechanical model with such a difficulty is constructed. This model is a
simplified analog of the large-N approximation to the -model
in 6-dimensional space-time. It is necessary to introduce an indefinite inner
product to renormalize the theory. The mathematical results of the theory of
Pontriagin spaces are essentially used. It is remarkable that not only the
field but also the canonically conjugated momentum become well-defined
operators after adding counterterms.Comment: 13 pages, LaTe
States and Observables in Semiclassical Field Theory: a Manifestly Covariant Approach
A manifestly covariant formulation of quantum field Maslov complex-WKB theory
(semiclassical field theory) is investigated for the case of scalar field. The
main object of the theory is "semiclassical bundle". Its base is the set of all
classical states, fibers are Hilbert spaces of quantum states in the external
field. Semiclassical Maslov states may be viewed as points or surfaces on the
semiclassical bundle. Semiclassical analogs of QFT axioms are formulated. A
relationship between covariant semiclassical field theory and Hamiltonian
formulation is discussed. The constructions of axiomatic field theory
(Schwinger sources, Bogoliubov -matrix, Lehmann-Symanzik-Zimmermann
-functions) are used in constructing the covariant semiclassical theory. A
new covariant formulation of classical field theory and semiclassical
quantization proposal are discussed.Comment: 20 pages, LaTeX, margins are corrected due to problems with viewing
PostScript fil
HIGH ORDER BEHAVIOUR OF PERTURBATION RECURSIVE RELATIONS
The problem of large order behaviour of perturbation theory for quantum
mechanical systems is considered. A new approach to it is developed. An
explicit mechanism showing the connection between large order recursive
relations and classical euclidean equations of motion is found. Large order
asymptotics of the solution to the recursive relations is constructed. The
developed method is applicable to the excited states, as well as to the ground
state. Singular points of the obtained asymptotics of the perturbation series
for eigenfunctions and density matrices are investigated and formulas being
valid near such points are obtained.Comment: 30 pages, LaTeX, 6 figures can be obtained from the autho
LARGE ORDER ASYMPTOTICS OF SEMICLASSICAL EXPANSION: A NEW APPROACH
A new approach to the problem of finding the asymptotical behaviour of large
orders of semiclassical expansion is suggested. Asymptotics of high orders not
only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one
can apply not only functional integral technique, which has been used up to
now, but also method of direct analysis of the semiclassical expansion
recursive relations.Comment: 24 pages, LaTeX, 4 figures can be obtained from the author, revised
russian version is submitted to Yadernaya Fizik
Instability of Space-Time due to Euclidean Wormholes
The problem of topology change transitions in quantum gravity is discussed.
We argue that the contribution of the Giddings-Strominger wormhole to the
Euclidean path integral is pure imaginary. This is checked by two techniques:
by the functional integral approach and by the analysis of the Wheeler-De Witt
equation. We present also a simple quantum mechanical model which shares many
features of the system consisting of parent and baby universes. In this simple
model, we show that quantum coherence is completely lost and obtain the
equation for the effective density matrix of the ''parent universe''.Comment: 9 pages in LaTeX, 3 figures in PostScript, to appear in Proceedings
of the 9th International Seminar "QUARKS-96
Renormalization of the Semiclassical Hamiltonian Field Theory
The Hamiltonian approach to the quantum field theory is considered. Since
there are additional difficulties such as the Haag theorem and Stueckelberg
divergences, renormalization of the time-dependent dynamical quantum field
theory is much more complicated than renormalization of the S-matrix. It is
necessary to consider the regularized theory with ultraviolet and infrared
cutoffs and impose the conditions not only on the dependence of the Hamiltonian
on the cutoffs (as usual) but also on the dependence of the initial states. It
happens that one should consider the initial states to be singulary dependent
on the cutoffs in order to avoid the Stueckelberg divergences. Different types
of semiclassical approximations to quantum theory are discussed. It happens
that the method of quantizing classical solutions to field equations
corresponds not to the WKB-approach but to the complex-WKB theory. The problem
of imposing conditions on the semiclassical initial states is discussed.
Different prescriptions for choice of initial conditions are analysed.Comment: Talk presented at the International Seminar "Quarks-98", Suzdal,
Russia, May 17-24, 1998, 12 pages in LaTeX, 1 postscript figur
A Negative Mode About Euclidean Wormhole
Wormholes -- solutions to the euclidean Einstein equations with non-trivial
topology -- are usually assumed to make real contributions to amplitudes in
quantum gravity. However, we find a negative mode among fluctuations about the
Giddings-Strominger wormhole solution. Hence, the wormhole contribution to the
euclidean functional integral is argued to be purely imaginary rather than
real, which suggests the interpretation of the wormhole as describing the
instability of a large universe against the emission of baby universes.Comment: 9 pages in LaTeX, 1 figure in PostScrip
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