33,968 research outputs found
Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branes
The principles of a previously developed formalism for the covariant
treatment of multi-scalar fields for which (as in a nonlinear sigma model) the
relevant target space is not of affine type -- but curved -- are recapitulated.
Their application is extended from ordinary harmonic models to a more general
category of "harmonious" field models, with emphasis on cases in which the
field is confined to a string or higher brane worldsheet, and for which the
relevant internal symmetry group is non Abelian, so that the conditions for
conservation of the corresponding charge currents become rather delicate,
particularly when the symmetry is gauged. Attention is also given to the
conditions for conservation of currents of a different kind -- representing
surface fluxes of generalised momentum or energy -- associated with symmetries
not of the internal target space but of the underlying spacetime background
structure, including the metric and any relevant gauge field. For the
corresponding current to be conserved the latter need not be manifestly
invariant: preservation modulo a gauge adjustment will suffice. The simplest
case is that of "strong" symmetry, meaning invariance under the action of an
effective Lie derivative (an appropriately gauge adjusted modification of an
ordinary Lie derivative). When the effective symmetry is of the more general
"weak" kind, the kinetic part of the current is not conserved by itself but
only after being supplemented by a suitable contribution from the background.Comment: 27 pages Latex (color
The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics
The natural relativistic generalisation of Landau's two constituent
superfluid theory can be formulated in terms of a Lagrangian that is given
as a function of the entropy current 4-vector and the gradient
of the superfluid phase scalar. It is shown that in the ``cool"
regime, for which the entropy is attributable just to phonons (not rotons), the
Lagrangian function is given by an expression of the
form where represents the pressure as a function just of
in the (isotropic) cold limit. The entropy current dependent
contribution represents the generalised pressure of the (non-isotropic)
phonon gas, which is obtained as the negative of the corresponding grand
potential energy per unit volume, whose explicit form has a simple algebraic
dependence on the sound or ``phonon" speed that is determined by the cold
pressure function .Comment: 26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 199
Recent developments in Vorton Theory
This article provides a concise overview of recent theoretical results
concerning the theory of vortons, which are defined to be (centrifugally
supported) equilibrium configurations of (current carrying) cosmic string
loops. Following a presentation of the results of work on the dynamical
evolution of small circular string loops, whose minimum energy states are the
simplest examples of vortons, recent order of magnitude estimates of the
cosmological density of vortons produced in various kinds of theoretical
scenario are briefly summarised.Comment: 6 pages Latex. Contribution to 1996 Cosmology Meeting, Peyresq,
Franc
Renormalisation of gravitational self interaction for wiggly strings
It is shown that for any elastic string model with energy density and
tension , the divergent contribution from gravitational self interaction can
be allowed for by an action renormalisation proportional to . This
formula is applied to the important special case of a bare model of the
transonic type (characterised by a constant value of the product ) that
represents the macroscopically averaged effect of shortwavelength wiggles on an
underlying microscopic model of the Nambu-Goto type (characterised by ).Comment: 11 pages, Latex; original 8 page version extended to include
estimates of relevant orders of magnitude. To be published in Physical
Review,
Poly-essential and general Hyperelastic World (brane) models
This article provides a unified treatment of an extensive category of
non-linear classical field models whereby the universe is represented (perhaps
as a brane in a higher dimensional background) in terms of a structure of a
mathematically convenient type describable as hyperelastic, for which a
complete set of equations of motion is provided just by the energy-momentum
conservation law. Particular cases include those of a perfect fluid in
quintessential backgrounds of various kinds, as well as models of the elastic
solid kind that has been proposed to account for cosmic acceleration. It is
shown how an appropriately generalised Hadamard operator can be used to
construct a symplectic structure that controles the evolution of small
perturbations, and that provides a characteristic equation governing the
propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds.
The special case of a poly-essential model - the k-essential analogue of an
ordinary polytropic fluid - is examined and shown to be well behaved (like the
fluid) only if the pressure to density ratio is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005:
Micro and Macro Structures of Spacetim
Transonic Elastic Model for Wiggly Goto-Nambu String
The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic
string can be effectively represented by an elastic string model of exactly
transonic type (with energy density inversely proportional to its tension
) is shown to have a firm mathematical basis.Comment: 8 pages, plain TeX, no figure
Symplectic structure for elastic and chiral conducting cosmic string models
This article is based on the covariant canonical formalism and corresponding
symplectic structure on phase space developed by Witten, Zuckerman and others
in the context of field theory. After recalling the basic principles of this
procedure, we construct the conserved bilinear symplectic current for generic
elastic string models. These models describe current carrying cosmic strings
evolving in an arbitrary curved background spacetime. Particular attention is
paid to the special case of the chiral string for which the worldsheet current
is null. Different formulations of the chiral string action are discussed in
detail, and as a result the integrability property of the chiral string is
clarified.Comment: 18 page
Cold, warm, and composite (cool) cosmic string models
The dynamical behaviour of a cosmic string is strongly affected by any
reduction of the effective string tension below the constant value
say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu
string model in terms of a fixed mass scale whose magnitude depends on that
of the Higgs field responsible for the existence of the string. Such a
reduction occurs in the standard "hot" cosmic string model in which the effect
of thermal perturbations of a simple Goto Nambu model is expressed by the
formula , where is the string
temperature. A qualitatively similar though analytically more complicated
tension reduction phenomenon occurs in "cold" conducting cosmic string models
where the role of the temperature is played by an effective chemical potential
that is constructed as the magnitude of the phase of a bosonic
condensate of the kind whose existence was first proposed by Witten. The
present article describes the construction and essential mechanical properties
of a category of "warm" cosmic string models that are intermediate between
these "hot" and "cold" extremes. These "warm" models are the string analogues
of the standard Landau model for a 2-constituent finite temperature superfluid,
and as such involve two independent currents interpretable as that of the
entropy on one hand and that of the bosonic condensate on the other. It is
surmised that the stationary (in particular ring) equilibrium states of such
"warm" cosmic strings may be of cosmological significance.Comment: 31 pages, Tex preprint version of manuscript subsequently published
(with editorial modifications) in Nuclear Physics
Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedure
The standard covariant differentiation procedure for fields in vector bundles
is generalised so as to be applicable to fields in general nonaffine bundles in
which the fibres may have an arbitrary nonlinear structure. In addition to the
usual requirement that the base space should be flat or endowed with its own
linear connection, and that there should be an ordinary gauge connection on the
bundle, it is necessary to require also that there should be an intrinsic,
bundle-group invariant connection on the fibre space. The procedure is based on
the use of an appropriate primary-field (i.e. section) independent connector
that is constructed in terms of the natural fibre-tangent-vector realisation of
the gauge connection. The application to gauged harmonic mappings will be
described in a following article.Comment: 17 page Latex file with some minor misprint corrections and added
color for article originally published in black and whit
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