1,330 research outputs found
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
Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism
We consider the algebra of spatial diffeomorphisms and gauge transformations
in the canonical formalism of General Relativity in the Ashtekar and ADM
variables. Modifying the Poisson bracket by including surface terms in
accordance with our previous proposal allows us to consider all local
functionals as differentiable. We show that closure of the algebra under
consideration can be achieved by choosing surface terms in the expressions for
the generators prior to imposing any boundary conditions. An essential point is
that the Poisson structure in the Ashtekar formalism differs from the canonical
one by boundary terms.Comment: 19 pages, Latex, amsfonts.sty, amssymb.st
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
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
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
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
Beyond Moore's technologies: operation principles of a superconductor alternative
The predictions of Moore's law are considered by experts to be valid until
2020 giving rise to "post-Moore's" technologies afterwards. Energy efficiency
is one of the major challenges in high-performance computing that should be
answered. Superconductor digital technology is a promising post-Moore's
alternative for the development of supercomputers. In this paper, we consider
operation principles of an energy-efficient superconductor logic and memory
circuits with a short retrospective review of their evolution. We analyze their
shortcomings in respect to computer circuits design. Possible ways of further
research are outlined.Comment: OPEN ACCES
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