26 research outputs found
Second central extension in Galilean covariant field theory
The second central extension of the planar Galilei group has been alleged to
have its origin in the spin variable. This idea is explored here by considering
local Galilean covariant field theory for free fields of arbitrary spin. It is
shown that such systems generally display only a trivial realization of the
second central extension. While it is possible to realize any desired value of
the extension parameter by suitable redefinition of the boost operator, such an
approach has no necessary connection to the spin of the basic underlying field.Comment: 6 pgs., late
On the linear forms of the Schrodinger equation
Generalizing the linearisation procedure used by Dirac and later by
L\'evy-Leblond, we derive the first-order non-relativistic wave equations for
particles of spin 1 and spin 3/2 starting from the Schrodinger equation
Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation
We report a modulational instability (MI) analysis of a mathematical model
appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media
beyond the so-called slowly varying envelope approximation. Theoretically
predicted MI properties are found to be in good agreement with numerical
simulation. The study shows the possibility of controlling the generation of MI
and formation of solitons in a cascaded quadratic-cubic media in the few cycle
regimes. We also find that stable propagation of soliton-like few-cycle pulses
in the medium is subject to the fulfilment of the modulation instability
criteria
Scaling anomaly in cosmic string background
We show that the classical scale symmetry of a particle moving in cosmic
string background is broken upon inequivalent quantization of the classical
system, leading to anomaly. The consequence of this anomaly is the formation of
single bound state in the coupling interval \gamma\in(-1,1). The inequivalent
quantization is characterized by a 1-parameter family of self-adjoint extension
parameter \omega. It has been conjectured that the formation of loosely bound
state in cosmic string background may lead to the so called anomalous
scattering cross section for the particles, which is usually seen in molecular
physics.Comment: 4 pages,1 figur
Dwelling on de Sitter
A careful reduction of the three-dimensional gravity to the Liouville
description is performed, where all gauge fixing and on-shell conditions come
from the definition of asymptotic de Sitter spaces. The roles of both past and
future infinities are discussed and the conditions space-time evolution imposes
on both Liouville fields are explicited. Space-times which correspond to
non-equivalent profiles of the Liouville field at past and future infinities
are shown to exist. The qualitative implications of this for any tentative dual
theory are presented.Comment: RevTeX 4, 8 pages, v3: Small clarifications on sections III and IV
and references added/corrected, v4: typo