1,490 research outputs found
Bering's proposal for boundary contribution to the Poisson bracket
It is shown that the Poisson bracket with boundary terms recently proposed by
Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the
present author (hep-th/9305133) if one omits terms free of Euler-Lagrange
derivatives ("annihilation principle"). This corresponds to another definition
of the formal product of distributions (or, saying it in other words, to
another definition of the pairing between 1-forms and 1-vectors in the formal
variational calculus). We extend the formula (initially suggested by Bering
only for the ultralocal case with constant coefficients) onto the general
non-ultralocal brackets with coefficients depending on fields and their spatial
derivatives. The lack of invariance under changes of dependent variables (field
redefinitions) seems a drawback of this proposal.Comment: 18 pages, LaTeX, amssym
Axiomatic formulations of nonlocal and noncommutative field theories
We analyze functional analytic aspects of axiomatic formulations of nonlocal
and noncommutative quantum field theories. In particular, we completely clarify
the relation between the asymptotic commutativity condition, which ensures the
CPT symmetry and the standard spin-statistics relation for nonlocal fields, and
the regularity properties of the retarded Green's functions in momentum space
that are required for constructing a scattering theory and deriving reduction
formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem
for analytic functionals. We also discuss the possibility of using analytic
test functions to extend the Wightman axioms to noncommutative field theory,
where the causal structure with the light cone is replaced by that with the
light wedge. We explain some essential peculiarities of deriving the CPT and
spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure
Two classes of generalized functions used in nonlocal field theory
We elucidate the relation between the two ways of formulating causality in
nonlocal quantum field theory: using analytic test functions belonging to the
space (which is the Fourier transform of the Schwartz space )
and using test functions in the Gelfand-Shilov spaces . We prove
that every functional defined on has the same carrier cones as its
restrictions to the smaller spaces . As an application of this
result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular
generalized functions of tempered growth and obtain the corresponding extension
of Vladimirov's algebra of functions holomorphic on a tubular domain.Comment: AMS-LaTeX, 12 pages, no figure
Twisted convolution and Moyal star product of generalized functions
We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure
Towards a Generalized Distribution Formalism for Gauge Quantum Fields
We prove that the distributions defined on the Gelfand-Shilov spaces, and
hence more singular than hyperfunctions, retain the angular localizability
property. Specifically, they have uniquely determined support cones. This
result enables one to develop a distribution-theoretic techniques suitable for
the consistent treatment of quantum fields with arbitrarily singular
ultraviolet and infrared behavior. The proofs covering the most general case
are based on the use of the theory of plurisubharmonic functions and
Hormander's estimates.Comment: 12 p., Department of Theoretical Physics, P.N.Lebedev Physical
Institute, Leninsky prosp. 53, Moscow 117924, Russi
Superconducting Phase Domains for Memory Applications
In this work we study theoretically the properties of S-F/N-sIS type
Josephson junctions in the frame of the quasiclassical Usadel formalism. The
structure consists of two superconducting electrodes (S), a tunnel barrier (I),
a combined normal metal/ferromagnet (N/F) interlayer and a thin superconducting
film (s). We demonstrate the breakdown of a spatial uniformity of the
superconducting order in the s-film and its decomposition into domains with a
phase shift . The effect is sensitive to the thickness of the s layer
and the widths of the F and N films in the direction along the sIS interface.
We predict the existence of a regime where the structure has two energy minima
and can be switched between them by an electric current injected laterally into
the structure. The state of the system can be non-destructively read by an
electric current flowing across the junction
Josephson effect in SIFS-tunnel junctions with domain walls in weak link region
We study theoretically the properties of SIFS type Josephson junctions
composed of two superconducting (S) electrodes separated by an insulating layer
(I) and a ferromagnetic (F) film consisting of periodic magnetic domains
structure with antiparallel magnetization directions in neighboring domains.
The two-dimensional problem in the weak link area is solved analytically in the
framework of the linearized quasiclassical Usadel equations. Based on this
solution, the spatial distributions of the critical current density,
in the domains and critical current, of SIFS structures are calculated
as a function of domain wall parameters, as well as the thickness, and
the width, of the domains. We demonstrate that
dependencies exhibit damped oscillations with the ratio of the decay length,
and oscillation period, being a function of the
parameters of the domains, and this ratio may take any value from zero to
unity. Thus, we propose a new physical mechanism that may explain the essential
difference between and observed experimentally in various
types of SFS Josephson junctions.Comment: The paper will be published in JETP letters vol 101, issue 11, 201
PCT, spin and statistics, and analytic wave front set
A new, more general derivation of the spin-statistics and PCT theorems is
presented. It uses the notion of the analytic wave front set of
(ultra)distributions and, in contrast to the usual approach, covers nonlocal
quantum fields. The fields are defined as generalized functions with test
functions of compact support in momentum space. The vacuum expectation values
are thereby admitted to be arbitrarily singular in their space-time dependence.
The local commutativity condition is replaced by an asymptotic commutativity
condition, which develops generalizations of the microcausality axiom
previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the
original published paper, but with corrected typos and slight improvements in
the exposition. The proof of Theorem 5 stated in the paper has been published
in J. Math. Phys. 45 (2004) 1944-195
Quantum field theory with a fundamental length: A general mathematical framework
We review and develop a mathematical framework for nonlocal quantum field
theory (QFT) with a fundamental length. As an instructive example, we reexamine
the normal ordered Gaussian function of a free field and find the primitive
analyticity domain of its n-point vacuum expectation values. This domain is
smaller than the usual future tube of local QFT, but we prove that in
difference variables, it has the same structure of a tube whose base is the
(n-1)-fold product of a Lorentz invariant region. It follows that this model
satisfies Wightman-type axioms with an exponential high-energy bound which does
not depend on n, contrary to the claims in the literature. In our setting, the
Wightman generalized functions are defined on test functions analytic in the
complex l-neighborhood of the real space, where l is an n-independent constant
playing the role of a fundamental length, and the causality condition is
formulated with the use of an analogous function space associated with the
light cone. In contrast to the scheme proposed by Bruning and Nagamachi [J.
Math. Phys. 45 (2004) 2199] in terms of ultra-hyperfunctions, the presented
theory obviously becomes local as l tends to zero.Comment: 25 pages, v2: updated to match J. Math. Phys. versio
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