1,206 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
Masses and Internal Structure of Mesons in the String Quark Model
The relativistic quantum string quark model, proposed earlier, is applied to
all mesons, from pion to , lying on the leading Regge trajectories
(i.e., to the lowest radial excitations in terms of the potential quark
models). The model describes the meson mass spectrum, and comparison with
measured meson masses allows one to determine the parameters of the model:
current quark masses, universal string tension, and phenomenological constants
describing nonstring short-range interaction. The meson Regge trajectories are
in general nonlinear; practically linear are only trajectories for light-quark
mesons with non-zero lowest spins. The model predicts masses of many new
higher-spin mesons. A new meson is predicted with mass 1910 Mev. In
some cases the masses of new low-spin mesons are predicted by extrapolation of
the phenomenological short-range parameters in the quark masses. In this way
the model predicts the mass of to be MeV, and
the mass of to be MeV (the potential model predictions
are 100 Mev lower). The relativistic wave functions of the composite mesons
allow one to calculate the energy and spin structure of mesons. The average
quark-spin projections in polarized -meson are twice as small as the
nonrelativistic quark model predictions. The spin structure of reveals an
80% violation of the flavour SU(3). These results may be relevant to
understanding the ``spin crises'' for nucleons.Comment: 30 pages, REVTEX, 6 table
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
Non-Localizability and Asymptotic Commutativity
The mathematical formalism commonly used in treating nonlocal highly singular
interactions is revised. The notion of support cone is introduced which
replaces that of support for nonlocalizable distributions. Such support cones
are proven to exist for distributions defined on the Gelfand-Shilov spaces
, where . This result leads to a refinement of previous
generalizations of the local commutativity condition to nonlocal quantum
fields. For string propagators, a new derivation of a representation similar to
that of K\"{a}llen-Lehmann is proposed. It is applicable to any initial and
final string configurations and manifests exponential growth of spectral
densities intrinsic in nonlocalizable theories.Comment: This version is identical to the initial one whose ps and pdf files
were unavailable, with few corrections of misprint
Proton-neutron pairing in the deformed BCS approach
We examine isovector and isoscalar proton-neutron pairing correlations for
the ground state of even-even Ge isotopes with mass number A=64-76 within the
deformed BCS approach. For N=Z 64Ge the BCS solution with only T=0
proton-neutron pairs is found. For other nuclear systems (N>Z) a coexistence of
a T=0 and T=1 pairs in the BCS wave function is observed. A problem of fixing
of strengths of isoscalar and isovector pairing interactions is addressed. A
dependence of number of like and unlike pairs in the BCS ground state on the
difference between number of neutrons and protons is discussed. We found that
for nuclei with N much bigger than Z the effect of proton-neutron pairing is
small but not negligible.Comment: 24 pages, 6 figure
Tagging High Energy Photons in the H1 Detector at HERA
Measures taken to extend the acceptance of the H1 detector at HERA for
photoproduction events are described. These will enable the measurement of
electrons scattered in events in the high y range 0.85 < y < 0.95 in the 1998
and 1999 HERA run period. The improvement is achieved by the installation of an
electromagnetic calorimeter, the ET8, in the HERA tunnel close to the electron
beam line 8 m downstream of the H1 interaction point in the electron direction.
The ET8 will allow the study of tagged gamma p interactions at centre-of-mass
energies significantly higher than those previously attainable. The calorimeter
design and expected performance are discussed, as are results obtained using a
prototype placed as close as possible to the position of the ET8 during the
1996 and 1997 HERA running.Comment: 13 pages, 13 figure
A New High Energy Photon Tagger for the H1 - Detector at HERA
The H1 detector at HERA has been upgraded by the addition of a new
electromagnetic calorimeter. This is installed in the HERA tunnel close to the
electron beam line at a position 8m from the interaction point in the electron
beam direction. The new calorimeter extends the acceptance for tagged
photoproduction events to the high y range, 0.85 < y < 0.95, and thus
significantly improves the capability of H1 to study high energy gamma-p
processes. The calorimeter design, performance and first results obtained
during the 1996-1999 HERA running are described.Comment: 17 pages, 16 figure
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