64,384 research outputs found
RQM description of PS meson form factors, constraints from space-time translations, and underlying dynamics
The role of Poincar\'e covariant space-time translations is investigated in
the case of the pseudoscalar-meson charge form factors. It is shown that this
role extends beyond the standard energy-momentum conservation, which is
accounted for in all relativistic quantum mechanics calculations. It implies
constraints that have been largely ignored until now but should be fulfilled to
ensure the full Poincar\'e covariance. The violation of these constraints,
which is more or less important depending on the form of relativistic quantum
mechanics that is employed, points to the validity of using a single-particle
current, which is generally assumed in calculations of form factors. In short,
these constraints concern the relation of the momentum transferred to the
constituents to the one transferred to the system. How to account for the
related constraints, as well as restoring the equivalence of different
relativistic quantum mechanics approaches in estimating form factors, is
discussed. Some conclusions relative to the underlying dynamics are given in
the pion case.Comment: 37 pages, 13 figures; figures completed for notations, revised text
with better emphasis on differences with previous works; accepted for
publication in EPJ
Form factors in relativistic quantum mechanics: constraints from space-time translations
The comparison of form factors calculated from a single-particle current in
different relativistic quantum mechanic approaches evidences tremendous
discrepancies. The role of constraints coming from space-time translations is
considered here with this respect. It is known that invariance under these
translations implies the energy-momentum conservation relation that is usually
assumed to hold globally. Transformations of the current under these
translations, which lead to this result, also imply constraints that have been
ignored so far in relativistic quantum mechanic approaches. An implementation
of these constraints is discussed in the case of a model with two scalar
constituents. It amounts to incorporate selected two-body currents to all
orders in the interaction. Discrepancies for form factors in different
approaches can thus be removed, contributing to restore the equivalence of
different approaches. Results for the standard front-form approach ()
are found to fulfill the constraints and are therefore unchanged. The relation
with results from a dispersion-relation approach is also made.Comment: 8 pages, 5 figures; to be published in the proceedings of LC2008;
Light Cone 2008. Relativistic Nuclear and Particle Physics, Mulhouse : France
(2008
Z-graded weak modules and regularity
It is proved that if any Z-graded weak module for vertex operator algebra V
is completely reducible, then V is rational and C_2-cofinite. That is, V is
regular. This gives a natural characterization of regular vertex operator
algebras.Comment: 9 page
Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra
The purpose of this paper is to generalize Zhu's theorem about characters of
modules over a vertex operator algebra graded by integer conformal weights, to
the setting of a vertex operator superalgebra graded by rational conformal
weights. To recover SL_2(Z)-invariance of the characters it turns out to be
necessary to consider twisted modules alongside ordinary ones. It also turns
out to be necessary, in describing the space of conformal blocks in the
supersymmetric case, to include certain `odd traces' on modules alongside
traces and supertraces. We prove that the set of supertrace functions, thus
supplemented, spans a finite dimensional SL_2(Z)-invariant space. We close the
paper with several examples.Comment: 42 pages. Published versio
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