1,601 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
Boundary values as Hamiltonian variables. I. New Poisson brackets
The ordinary Poisson brackets in field theory do not fulfil the Jacobi
identity if boundary values are not reasonably fixed by special boundary
conditions. We show that these brackets can be modified by adding some surface
terms to lift this restriction. The new brackets generalize a canonical bracket
considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary
problem in hydrodynamics. Our definition of Poisson brackets permits to treat
boundary values of a field on equal footing with its internal values and
directly estimate the brackets between both surface and volume integrals. This
construction is applied to any local form of Poisson brackets. A prescription
for delta-function on closed domains and a definition of the {\it full}
variational derivative are proposed.Comment: 26 pages, LaTex, IHEP 93-4
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
Relativistic quasiparticle time blocking approximation. II. Pygmy dipole resonance in neutron-rich nuclei
Theoretical studies of low-lying dipole strength in even-even spherical
nuclei within the relativistic quasiparticle time blocking approximation
(RQTBA) are presented. The RQTBA developed recently as an extension of the
self-consistent relativistic quasiparticle random phase approximation (RQRPA)
enables one to investigate effects of coupling of two-quasiparticle excitations
to collective vibrations within a fully consistent calculation scheme based on
covariant energy density functional theory. Dipole spectra of even-even
Sn -- Sn and Ni -- Ni isotopes calculated within
both RQRPA and RQTBA show two well separated collective structures: the
higher-lying giant dipole resonance (GDR) and the lower-lying pygmy dipole
resonance (PDR) which can be identified by a different behavior of the
transition densities of states in these regions.Comment: 28 pages, 13 figure
Knizhnik-Zamolodchikov-type equations for gauged WZNW models
We study correlation functions of coset constructions by utilizing the method
of gauge dressing. As an example we apply this method to the minimal models and
to the Witten 2D black hole. We exhibit a striking similarity between the
latter and the gravitational dressing. In particular, we look for logarithmic
operators in the 2D black hole.Comment: 24 pages, latex, no figures. More discussion of logarithmic operators
was adde
Benchmarks for the Forward Observables at RHIC, the Tevatron-run II and the LHC
We present predictions on the total cross sections and on the ratio of the
real part to the imaginary part of the elastic amplitude (rho parameter) for
present and future pp and pbar p colliders, and on total cross sections for
gamma p -> hadrons at cosmic-ray energies and for gamma gamma-> hadrons up to
sqrt{s}=1 TeV. These predictions are based on an extensive study of possible
analytic parametrisations invoking the biggest hadronic dataset available at
t=0. The uncertainties on total cross sections, including the systematic errors
due to contradictory data points from FNAL, can reach 1.9% at RHIC, 3.1% at the
Tevatron, and 4.8% at the LHC, whereas those on the rho parameter are
respectively 5.4%, 5.2%, and 5.4%.Comment: 11 pages, 2 figures, 4 tables, RevTeX
The partition function versus boundary conditions and confinement in the Yang-Mills theory
We analyse dependence of the partition function on the boundary condition for
the longitudinal component of the electric field strength in gauge field
theories. In a physical gauge the Gauss law constraint may be resolved
explicitly expressing this component via an integral of the physical
transversal variables. In particular, we study quantum electrodynamics with an
external charge and SU(2) gluodynamics. We find that only a charge distribution
slowly decreasing at spatial infinity can produce a nontrivial dependence in
the Abelian theory. However, in gluodynamics for temperatures below some
critical value the partition function acquires a delta-function like dependence
on the boundary condition, which leads to colour confinement.Comment: 14 pages, RevTeX, submitted to Phys. Rev.
- âŠ