1,763 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
Spectroscopic features of low-energy excitations in skin nuclei
Systematic studies of dipole and other multipole excitations in stable and
exotic nuclei are discussed theoretically. Exploring the relation of the
strengths of low-energy dipole and quadrupole pygmy resonances to the thickness
of the neutron (proton) skin a close connection between static and dynamic
properties of the nucleus is observed. The fine structure of low-energy dipole
strength in 138Ba nucleus is revealed from E1 and spin-flip M1 strengths
distributions.Comment: A Talk given at the Int. Symposium 'Forefronts of Researches in
Exotic Nuclear Structures - Niigata2010 -', 1-4 March, 2010, Tokamachi,
Niigata, Japan; to be published in a volume of Modern Physics Letters A
(MPLA)
Pygmy dipole resonance in exotic nuclei
The evolution of the PDR strength with the neutron excess is investigated in
Sn isotopic and N=82 isotonic chains with regard to its possible connection
with the neutron skin thickness. For this purpose a recently proposed method
incorporating both HFB and multi-phonon QPM theory is applied. Analysis of the
corresponding neutron and proton dipole transition densities is presented.Comment: International Workshop on Nuclear Physics 28th Course - Radioactive
Beams, Nuclear Dynamics and Astrophysics, Ettore Majorana Center for
Scientific Cultur
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
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
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
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
Low-energy Dipole Excitations in Nuclei at the N=50,82 and Z=50 Shell Closures as Signatures for a Neutron Skin
Low-energy dipole excitations have been investigated theoretically in N=50,
several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method
incorporating both HFB and multi-phonon QPM theory is applied. A concentration
of one-phonon dipole strength located below the neutron emission threshold has
been calculated in these nuclei. The analysis of the corresponding neutron and
proton dipole transition densities allows to assign a genuine pattern to the
low-energy excitations and making them distinct from the conventional GDR
modes. Analyzing also the QRPA wave functions of the states we can identify
these excitations as Pygmy Dipole Resonance (PDR) modes, recently studied also
in Sn and N=82 nuclei. The results for N=50 are exploratory for an experimental
project designed for the bremsstrahlung facility at the ELBE accelerator.Comment: Nuclear Physics in Astrophysics III Conference, 26 - 31 March 2007,
Forschungszentrum Dresden-Rossendorf, German
- âŠ