537 research outputs found
Photon decay gamma->nu anti-nu in an external magnetic field
The process of the photon decay into the neutrino - antineutrino pair in a
magnetic field is investigated. The amplitude and the probability are analysed
in the limits of relatively small and strong fields. The probability is
suppressed by a factor (G_F m^2_e)^2 as compared with the probability of the
pure electromagnetic process gamma -> e- e+. However, the process with
neutrinos could play a role of an additional channel of stellar energy-loss.Comment: 8 pages, LaTeX, typos fixed, minor modifications, version accepted to
Physics Letters
Electromagnetic Catalysis of the Radiative Decay of the Axion
The radiative decay of the axion is investigated in an
external electromagnetic field in DFSZ model in which axion couples to both
quarks and leptons at tree level. The decay probability is strongly catalyzed
by the external field, namely, the field removes the main suppression caused by
the smallness of the axion mass.Comment: Minor revision, references added, to be published in Phys.Lett.
Axion decay in a strong magnetic field
The axion decay into charged fermion-antifermion pair is
studied in external crossed and magnetic fields. The result we have obtained
can be of use to re-examine the lower limit on the axion mass in case of
possible existence of strong magnetic fields at the early Universe stage.Comment: 6 pages, latex. Amended version, references added, to be published in
Phys.Lett.
A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear \W_{\rm KP} Algebra
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson
structures obtained from a generalized Adler map in the space of formal
pseudodifferential symbols with noninteger powers. The resulting \W-algebra
is a one-parameter deformation of \W_{\rm KP} admitting a central extension
for generic values of the parameter, reducing naturally to \W_n for special
values of the parameter, and contracting to the centrally extended
\W_{1+\infty}, \W_\infty and further truncations. In the classical limit,
all algebras in the one-parameter family are equivalent and isomorphic to
\w_{\rm KP}. The reduction induced by setting the spin-one field to zero
yields a one-parameter deformation of \widehat{\W}_\infty which contracts to
a new nonlinear algebra of the \W_\infty-type.Comment: 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92,
KUL-TF-92/20. [version just replaced was truncated by some mailer
Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
Darboux coordinates are constructed on rational coadjoint orbits of the
positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by
the values of the spectral parameters at the divisors corresponding to
eigenvector line bundles over the associated spectral curves, defined within a
given matrix representation. A Liouville generating function is obtained in
completely separated form and shown, through the Liouville-Arnold integration
method, to lead to the Abel map linearization of all Hamiltonian flows induced
by the spectral invariants. Serre duality is used to define a natural
symplectic structure on the space of line bundles of suitable degree over a
permissible class of spectral curves, and this is shown to be equivalent to the
Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general
construction is given for or , with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case is shown to reproduce
the classical integration methods for finite dimensional systems defined on
quadrics, as well as the quasi-periodic solutions of the cubically nonlinear
Schr\"odinger equation. For , the method is applied to the
computation of quasi-periodic solutions of the two component coupled nonlinear
Schr\"odinger equation.Comment: 61 pg
Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
We construct affinization of the algebra of ``complex size''
matrices, that contains the algebras for integral values of the
parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra
results in the quadratic Gelfand--Dickey structure on the
Poisson--Lie group of all pseudodifferential operators of fractional order.
This construction is extended to the simultaneous deformation of orthogonal and
simplectic algebras that produces self-adjoint operators, and it has a
counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure
Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
The matrix version of the -KdV hierarchy has been recently
treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian
symmetry reduction applied to a Poisson submanifold in the dual of the Lie
algebra . Here a
series of extensions of this matrix Gelfand-Dickey system is derived by means
of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra
using the natural
embedding for any positive integer. The
hierarchies obtained admit a description in terms of a matrix
pseudo-differential operator comprising an -KdV type positive part and a
non-trivial negative part. This system has been investigated previously in the
case as a constrained KP system. In this paper the previous results are
considerably extended and a systematic study is presented on the basis of the
Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson
brackets and makes clear the conformal (-algebra) structures related to
the KdV type hierarchies. Discrete reductions and modified versions of the
extended -KdV hierarchies are also discussed.Comment: 60 pages, plain TE
Non-Local Matrix Generalizations of W-Algebras
There is a standard way to define two symplectic (hamiltonian) structures,
the first and second Gelfand-Dikii brackets, on the space of ordinary linear
differential operators of order , . In this paper, I consider in detail the case where the are
-matrix-valued functions, with particular emphasis on the (more
interesting) second Gelfand-Dikii bracket. Of particular interest is the
reduction to the symplectic submanifold . This reduction gives rise to
matrix generalizations of (the classical version of) the {\it non-linear}
-algebras, called -algebras. The non-commutativity of the
matrices leads to {\it non-local} terms in these -algebras. I show
that these algebras contain a conformal Virasoro subalgebra and that
combinations of the can be formed that are -matrices of
conformally primary fields of spin , in analogy with the scalar case .
In general however, the -algebras have a much richer structure than
the -algebras as can be seen on the examples of the {\it non-linear} and
{\it non-local} Poisson brackets of any two matrix elements of or
which I work out explicitly for all and . A matrix Miura transformation
is derived, mapping these complicated second Gelfand-Dikii brackets of the
to a set of much simpler Poisson brackets, providing the analogue of the
free-field realization of the -algebras.Comment: 43 pages, a reference and a remark on the conformal properties for
adde
Real clocks and the Zeno effect
Real clocks are not perfect. This must have an effect in our predictions for
the behaviour of a quantum system, an effect for which we present a unified
description encompassing several previous proposals. We study the relevance of
clock errors in the Zeno effect, and find that generically no Zeno effect can
be present (in such a way that there is no contradiction with currently
available experimental data). We further observe that, within the class of
stochasticities in time addressed here, there is no modification in emission
lineshapes.Comment: 12 a4 pages, no figure
Softly broken supersymmetric Yang-Mills theories: Renormalization and non-renormalization theorems
We present a minimal version for the renormalization of softly broken
Super-Yang-Mills theories using the extended model with a local gauge coupling.
It is shown that the non-renormalization theorems of the case with unbroken
supersymmetry are valid without modifications and that the renormalization of
soft-breaking parameters is completely governed by the renormalization of the
supersymmetric parameters. The symmetry identities in the present context are
peculiar, since the extended model contains two anomalies: the Adler-Bardeen
anomaly of the axial current and an anomaly of supersymmetry in the presence of
the local gauge coupling. From the anomalous symmetries we derive the exact
all-order expressions for the beta functions of the gauge coupling and of the
soft-breaking parameters. They generalize earlier results to arbitrary
normalization conditions and imply the NSVZ expressions for a specific
normalization condition on the coupling.Comment: 24 pages, LaTeX, v2: one reference adde
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