17,345 research outputs found
General properties of the decay amplitudes for massless particles
We derive the kinematical constraints which characterize the decay of any
massless particle in flat spacetime. We show that in perturbation theory the
decay probabilities of photons and Yang-Mills bosons vanish to all orders; the
decay probability of the graviton vanishes to one-loop order for graviton loops
and to all orders for matter loops. A general power counting argument indicates
in which conditions a decay of a massless particle could be possible: the
lagrangian should contain a self-coupling without derivatives and with a
coupling constant of positive mass dimension.Comment: Latex file, 32 pages, to appear in Nucl. Phys. B. Improved
presentation, some additional results and references, typos correcte
QFT with Twisted Poincar\'e Invariance and the Moyal Product
We study the consequences of twisting the Poincare invariance in a quantum
field theory. First, we construct a Fock space compatible with the twisting and
the corresponding creation and annihilation operators. Then, we show that a
covariant field linear in creation and annihilation operators does not exist.
Relaxing the linearity condition, a covariant field can be determined. We show
that it is related to the untwisted field by a unitary transformation and the
resulting n-point functions coincide with the untwisted ones. We also show that
invariance under the twisted symmetry can be realized using the covariant field
with the usual product or by a non-covariant field with a Moyal product. The
resulting S-matrix elements are shown to coincide with the untwisted ones up to
a momenta dependent phase.Comment: 11 pages, references adde
q-Quaternions and q-deformed su(2) instantons
We construct (anti)instanton solutions of a would-be q-deformed su(2)
Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant
noncommutative space] by reinterpreting the function algebra on the latter as a
q-quaternion bialgebra. Since the (anti)selfduality equations are covariant
under the quantum group of deformed rotations, translations and scale change,
by applying the latter we can generate new solutions from the one centered at
the origin and with unit size. We also construct multi-instanton solutions. As
they depend on noncommuting parameters playing the roles of `sizes' and
`coordinates of the centers' of the instantons, this indicates that the moduli
space of a complete theory will be a noncommutative manifold. Similarly, gauge
transformations should be allowed to depend on additional noncommutative
parameters.Comment: Latex file, 39 pages. Final version appeared in JM
q-Deformed quaternions and su(2) instantons
We have recently introduced the notion of a q-quaternion bialgebra and shown
its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4.
Adopting the available differential geometric tools on the latter and the
quaternion language we have formulated and found solutions of the
(anti)selfduality equation [instantons and multi-instantons] of a would-be
deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on
some noncommuting parameters, indicating that the moduli space of a complete
theory should be a noncommutative manifold. We summarize these results and add
an explicit comparison between the two SO_q(4)-covariant differential calculi
on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi-
(resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially
coincide.Comment: Latex file, 18 page
On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups
We show that, if there exists a realization of a Hopf algebra in a
-module algebra , then one can split their cross-product into the tensor
product algebra of itself with a subalgebra isomorphic to and commuting
with . This result applies in particular to the algebra underlying
inhomogeneous quantum groups like the Euclidean ones, which are obtained as
cross-products of the quantum Euclidean spaces with the quantum groups
of rotation of , for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.
Unidirectional Rotation Neurones in the Optomotor System of the Crab, Carcinus
1. Among the optomotor fibres to the eye muscles in Carcinus a class was found which responds to unidirectional fast rotations around various body axes. All had large signals and are therefore of large diameter.
2. In one set of these fibres which fires especially for rotations around the dorsoventral axis, it could be shown that discharges take place especially during accelerations and that, when a rotation in the null direction is suddenly stopped, a short discharge occurs. The fibres for other axes behave in a similar manner.
3. For rotations around the ventro-dorsal axis, but not for other directions, mediumsized fibres are present which, in contrast to the fast fibres, respond to visual stimulation, as well as to body rotations in darkness, thus combining the input properties of the unidirectional fast rotatory and the unidirectional purely optokinetic small fibres. Their sensitivity to visual input is for low rotation velocities, to body rotations is for high rotation velocities
Factors Regulating the Discharge Frequency in Optomotor Fibres Of Carcinus Maenas
The influence of the excited state of the animal on various motor neurone discharges and accompanying muscle action potentials was studied in the eyestalk of the crab, Carcinus maenas.
In most cases large increases in firing frequency could be obtained during such states. An exception is the tonic eye-withdrawal system in which an inhibitory effect is caused.
A pronounced difference in habituation to constant stimuli between spring and summer was found for the position fibres; in spring it was slow and in summer much quicker
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