69 research outputs found
Casimir operators of the exceptional group : the chain
Expressions are given for the Casimir operators of the exceptional group
in a concise form similar to that used for the classical groups. The
chain is used to label the generators of
in terms of the adjoint and spinor representations of and to express the
26-dimensional representation of in terms of the defining representation
of . Casimir operators of any degree are obtained and it is shown that
a basis consists of the operators of degree 2, 6, 8 and 12
Group theory factors for Feynman diagrams
We present algorithms for the group independent reduction of group theory
factors of Feynman diagrams. We also give formulas and values for a large
number of group invariants in which the group theory factors are expressed.
This includes formulas for various contractions of symmetric invariant tensors,
formulas and algorithms for the computation of characters and generalized
Dynkin indices and trace identities. Tables of all Dynkin indices for all
exceptional algebras are presented, as well as all trace identities to order
equal to the dual Coxeter number. Further results are available through
efficient computer algorithms (see http://norma.nikhef.nl/~t58/ and
http://norma.nikhef.nl/~t68/ ).Comment: Latex (using axodraw.sty), 47 page
The electron-nucleon cross section in reactions
We examine commonly used approaches to deal with the scattering of electrons
from a bound nucleon. Several prescriptions are shown to be related by gauge
transformations. Nevertheless, due to current non-conservation, they yield
different results. These differences reflect the size of the uncertainty that
persists in the interpretation of experiments.Comment: 6 pp (10 in preprint form), ReVTeX, (+ 4 figures, uuencoded
Graded contractions of bilinear invariant forms of Lie algebras
We introduce a new construction of bilinear invariant forms on Lie algebras,
based on the method of graded contractions. The general method is described and
the -, -, and -contractions are
found. The results can be applied to all Lie algebras and superalgebras (finite
or infinite dimensional) which admit the chosen gradings. We consider some
examples: contractions of the Killing form, toroidal contractions of ,
and we briefly discuss the limit to new WZW actions.Comment: 15 page
Casimir invariants for the complete family of quasi-simple orthogonal algebras
A complete choice of generators of the center of the enveloping algebras of
real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is
obtained in a unified setting. The results simultaneously include the well
known polynomial invariants of the pseudo-orthogonal algebras , as
well as the Casimirs for many non-simple algebras such as the inhomogeneous
, the Newton-Hooke and Galilei type, etc., which are obtained by
contraction(s) starting from the simple algebras . The dimension of
the center of the enveloping algebra of a quasi-simple orthogonal algebra turns
out to be the same as for the simple algebras from which they come by
contraction. The structure of the higher order invariants is given in a
convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski"
elements in the enveloping algebras. As an example showing this approach at
work, the scheme is applied to recovering the Casimirs for the (3+1)
kinematical algebras. Some prospects on the relevance of these results for the
study of expansions are also given.Comment: 19 pages, LaTe
Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras
We present the eigenvalues of the Casimir invariants for the type I quantum
superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy
Dispersion Relations and Rescattering Effects in B Nonleptonic Decays
Recently, the final state strong interactions in nonleptonic B decays were
investigated in a formalism based on hadronic unitarity and dispersion
relations in terms of the off-shell mass squared of the meson. We consider
an heuristic derivation of the dispersion relations in the mass variables using
the reduction LSZ formalism and find a discrepancy between the spectral
function and the dispersive variable used in the recent works. The part of the
unitarity sum which describes final state interactions is shown to appear as
spectral function in a dispersion relation based on the analytic continuation
in the mass squared of one final particles. As an application, by combining
this formalism with Regge theory and SU(3) flavour symmetry we obtain
constraints on the tree and the penguin amplitudes of the decay .Comment: 17 pages, Latex, 2 figure
The off-shell electromagnetic form factors of pions and kaons in chiral perturbation theory
The off-shell electromagnetic vertex of a (pseudo-) scalar particle contains,
in general, two form factors F and G which depend, in addition to the squared
momentum transfer, on the invariant masses associated with the initial and
final legs of the vertex. Chiral perturbation theory to one loop is used to
calculate the off-shell form factors of pions and kaons. The formalism of
Gasser and Leutwyler, which was previously used to calculate the on-shell limit
of the form factor F, is extended to accommodate the most general form for
off-shell Green's functions in the pseudoscalar meson sector. We find that
chiral symmetry predicts that the form factors F of the charged pions and kaons
go off-shell in the same way, i.e., the off-shell slope at the real photon
point is given by the same new phenomenological constant .
Furthermore, it is shown that at order the form factor F of the
does not show any off-shell dependence. The form factors G are all related to
the form factors F in the correct fashion as required by the Ward-Takahashi
identity. Numerical results for different off-shell kinematics are presented.Comment: TRIUMF preprint TRI-PP-94-4, 25 pages in LaTeX + 10 figures
(uufile'd, compressed PostScript file appended at end, hardcopy available
from authors
Form factors and photoproduction amplitudes
We examine the use of phenomenological form factors in tree level amplitudes
for meson photoproduction. Two common recipes are shown to be fundamentally
incorrect. An alternate form consistent with gauge invariance and crossing
symmetry is proposed.Comment: To be published in PR
Virtual Compton scattering off the nucleon at low energies
We investigate the low-energy behavior of the four-point Green's function
describing virtual Compton scattering off the nucleon.
Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive
the leading terms of an expansion of the operator in the four-momenta and
of the initial and final photon, respectively.
The model-independent result is expressed in terms of the electromagnetic
form factors of the free nucleon, i.e., on-shell information which one obtains
from electron-nucleon scattering experiments.
Model-dependent terms appear in the operator at ,
whereas the orders and are
contained in the low-energy theorem for , i.e., no new
parameters appear.
We discuss the leading terms of the matrix element and comment on the use of
on-shell equivalent electromagnetic vertices in the calculation of ``Born
terms'' for virtual Compton scattering.Comment: 26 pages, RevTex, to appear in Phys. Rev.
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