11,386 research outputs found
(j,0)+(0,j) Covariant spinors and causal propagators based on Weinberg formalism
A pragmatic approach to constructing a covariant phenomenology of the
interactions of composite, high-spin hadrons is proposed. Because there are no
known wave equations without significant problems, we propose to construct the
phenomenology without explicit reference to a wave equation. This is done by
constructing the individual pieces of a perturbation theory and then utilizing
the perturbation theory as the definition of the phenomenology. The covariant
spinors for a particle of spin are constructed directly from Lorentz
invariance and the basic precepts of quantum mechanics following the logic put
forth originally by Wigner and developed by Weinberg. Explicit expressions for
the spinors are derived for j=1, 3/2 and 2. Field operators are constructed
from the spinors and the free-particle propagator is derived from the vacuum
expectation value of the time-order product of the field operators. A few
simple examples of model interactions are given. This provides all the
necessary ingredients to treat at a phenomenological level and in a covariant
manner particles of arbitrary spin.Comment: tex file, 52 page
Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis
We express the complex potential E and the metrical fields omega and gamma of
all stationary axisymmetric vacuum spacetimes that result from the application
of two successive quadruple-Neugebauer (or two double-Harrison) transformations
to Minkowski space in terms of data specified on the symmetry axis, which are
in turn easily expressed in terms of multipole moments. Moreover, we suggest
how, in future papers, we shall apply our approach to do the same thing for
those vacuum solutions that arise from the application of more than two
successive transformations, and for those electrovac solutions that have axis
data similar to that of the vacuum solutions of the Neugebauer family.
(References revised following response from referee.)Comment: 18 pages (REVTEX
Acoustics of tachyon Fermi gas
We consider a Fermi gas of free tachyons as a continuous medium and find
whether it satisfies the causality condition. There is no stable tachyon matter
with the particle density below critical value and the Fermi momentum
that depends on the tachyon mass . The pressure
and energy density cannot be arbitrary small, but the situation is
not forbidden. Existence of shock waves in tachyon gas is also discussed. At
low density the tachyon matter remains stable but no shock wave
do survive.Comment: 14 pages, 2 figures (color
Generating anisotropic fluids from vacuum Ernst equations
Starting with any stationary axisymmetric vacuum metric, we build anisotropic
fluids. With the help of the Ernst method, the basic equations are derived
together with the expression for the energy-momentum tensor and with the
equation of state compatible with the field equations. The method is presented
by using different coordinate systems: the cylindrical coordinates
and the oblate spheroidal ones. A class of interior solutions matching with
stationary axisymmetric asymptotically flat vacuum solutions is found in oblate
spheroidal coordinates. The solutions presented satisfy the three energy
conditions.Comment: Version published on IJMPD, title changed by the revie
On the degeneracies of the mass-squared differences for three-neutrino oscillations
Using an algebraic formulation, we explore two well-known degeneracies
involving the mass-squared differences for three-neutrino oscillations assuming
CP symmetry is conserved. For vacuum oscillation, we derive the expression for
the mixing angles that permit invariance under the interchange of two
mass-squared differences. This symmetry is most easily expressed in terms of an
ascending mass order. This can be used to reduce the parameter space by one
half in the absence of the MSW effect. For oscillations in matter, we derive
within our formalism the known approximate degeneracy between the standard and
inverted mass hierarchies in the limit of vanishing . This is done
with a mass ordering that permits the map .
Our techniques allow us to translate mixing angles in this mass order
convention into their values for the ascending order convention. Using this
dictionary, we demonstrate that the vacuum symmetry and the approximate
symmetry invoked for oscillations in matter are distinctly different.Comment: 5 pages, revised manuscrip
Fully Electrified Neugebauer Spacetimes
Generalizing a method presented in an earlier paper, we express the complex
potentials E and Phi of all stationary axisymmetric electrovac spacetimes that
correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) ,
where U = z^{2} + U_{1} z + U_{2} , V = V_{1} z + V_{2} , W = W_{1} z + W_{2} ,
in terms of the complex parameters U_{1}, V_{1}, W_{1}, U_{2}, V_{2} and W_{2},
that are directly associated with the various multipole moments. (Revised to
clarify certain subtle points.)Comment: 25 pages, REVTE
Velocity Tails for Inelastic Maxwell Models
We study the velocity distribution function for inelastic Maxwell models,
characterized by a Boltzmann equation with constant collision rate, independent
of the energy of the colliding particles. By means of a nonlinear analysis of
the Boltzmann equation, we find that the velocity distribution function decays
algebraically for large velocities, with exponents that are analytically
calculated.Comment: 4 pages, 2 figure
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
Integrability of generalized (matrix) Ernst equations in string theory
The integrability structures of the matrix generalizations of the Ernst
equation for Hermitian or complex symmetric -matrix Ernst potentials
are elucidated. These equations arise in the string theory as the equations of
motion for a truncated bosonic parts of the low-energy effective action
respectively for a dilaton and - matrix of moduli fields or for a
string gravity model with a scalar (dilaton) field, U(1) gauge vector field and
an antisymmetric 3-form field, all depending on two space-time coordinates
only. We construct the corresponding spectral problems based on the
overdetermined -linear systems with a spectral parameter and the
universal (i.e. solution independent) structures of the canonical Jordan forms
of their matrix coefficients. The additionally imposed conditions of existence
for each of these systems of two matrix integrals with appropriate symmetries
provide a specific (coset) structures of the related matrix variables. An
equivalence of these spectral problems to the original field equations is
proved and some approach for construction of multiparametric families of their
solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop
``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004,
Gallipoli (Lecce), Italy. Minor typos, language and references corrections.
To be published in the proceedings in Theor. Math. Phy
Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term
In this paper we show how the method of Zakharov transformations may be used
to analyze the stationary solutions of the Smoluchowski aggregation equation
for arbitrary homogeneous kernel. The resulting massdistributions are of
Kolmogorov type in the sense that they carry a constant flux of mass from small
masses to large. We derive a ``locality criterion'', expressed in terms of the
asymptotic properties of the kernel, that must be satisfied in order for the
Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads
to a gelation transition or not can be determined by computing the mass
capacity of the Kolmogorov spectrum. As an example, we compute the exact
stationary state for the family of
kernels, which includes both gelling and
non-gelling cases, reproducing the known solution in the case .
Surprisingly, the Kolmogorov constant is the same for all kernels in this
family.Comment: This article is an expanded version of a talk given at IHP workshop
"Dynamics, Growth and Singularities of Continuous Media", Paris July 2003.
Updated 01/04/04. Revised version with additional discussion, references
added, several typographical errors corrected. Revised version accepted for
publication by Phys. Rev.
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