1,638 research outputs found
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
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
Noncommutativity and theta-locality
In this paper, we introduce the condition of theta-locality which can be used
as a substitute for microcausality in quantum field theory on noncommutative
spacetime. This condition is closely related to the asymptotic commutativity
which was previously used in nonlocal QFT. Heuristically, it means that the
commutator of observables behaves at large spacelike separation like
, where is the noncommutativity parameter. The
rigorous formulation given in the paper implies averaging fields with suitable
test functions. We define a test function space which most closely corresponds
to the Moyal star product and prove that this space is a topological algebra
under the star product. As an example, we consider the simplest normal ordered
monomial and show that it obeys the theta-locality condition.Comment: LaTeX, 17 pages, no figures; minor changes to agree with published
versio
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
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
Investigation of Pygmy Dipole Resonances in the Tin Region
The evolution of the low-energy electromagnetic dipole response with the
neutron excess is investigated along the Sn isotopic chain within an approach
incorporating Hartree-Fock-Bogoljubov (HFB) and multi-phonon
Quasiparticle-Phonon-Model (QPM) theory. General aspects of the relationship of
nuclear skins and dipole sum rules are discussed. Neutron and proton transition
densities serve to identify the Pygmy Dipole Resonance (PDR) as a generic mode
of excitation. The PDR is distinct from the GDR by its own characteristic
pattern given by a mixture of isoscalar and isovector components. Results for
the Sn-Sn isotopes and the several N=82 isotones are presented.
In the heavy Sn-isotopes the PDR excitations are closely related to the
thickness of the neutron skin. Approaching Sn a gradual change from a
neutron to a proton skin is found and the character of the PDR is changed
correspondingly. A delicate balance between Coulomb and strong interaction
effects is found. The fragmentation of the PDR strength in Sn is
investigated by multi-phonon calculations. Recent measurements of the dipole
response in Sn are well reproduced.Comment: 41 pages, 10 figures, PR
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
Protected 0-pi states in SIsFS junctions for Josephson memory and logic
We study the peculiarities in current-phase relations (CPR) of the SIsFS
junction in the region of to transition. These CPR consist of two
independent branches corresponding to and states of the contact. We
have found that depending on the transparency of the SIs tunnel barrier the
decrease of the s-layer thickness leads to transformation of the CPR shape
going in the two possible ways: either one of the branches exists only in
discrete intervals of the phase difference or both branches are
sinusoidal but differ in the magnitude of their critical currents. We
demonstrate that the difference can be as large as under maintaining
superconductivity in the s layer. An applicability of these phenomena for
memory and logic application is discussed.Comment: 5 pages, 5 figure
Failure of microcausality in noncommutative field theories
We revisit the question of microcausality violations in quantum field theory
on noncommutative spacetime, taking as a sample
observable. Using methods of the theory of distributions, we precisely describe
the support properties of the commutator [O(x),O(y)] and prove that, in the
case of space-space noncommutativity, it does not vanish at spacelike
separation in the noncommuting directions. However, the matrix elements of this
commutator exhibit a rapid falloff along an arbitrary spacelike direction
irrespective of the type of noncommutativity. We also consider the star
commutator for this observable and show that it fails to vanish even at
spacelike separation in the commuting directions and completely violates
causality. We conclude with a brief discussion about the modified Wightman
functions which are vacuum expectation values of the star products of fields at
different spacetime points.Comment: LaTeX, 22 pages; v2: minor updates to agree with published version,
added referenc
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