541 research outputs found
Conformal p-branes as a Source of Structure in Spacetime
We discuss a model of a conformal p-brane interacting with the world volume
metric and connection. The purpose of the model is to suggest a mechanism by
which gravity coupled to p-branes leads to the formation of structure rather
than homogeneity in spacetime. Furthermore, we show that the formation of
structure is accompanied by the appearance of a multivalued cosmological
constant, i.e., one which may take on different values in different domains, or
cells, of spacetime. The above results apply to a broad class of non linear
gravitational lagrangians as long as metric and connection on the p-brane
manifold are treated as independent variables.Comment: 10 pages, ReVTeX, no figure
Axionic Membranes
A metal ring removed from a soap-water solution encloses a film of soap which
can be mathematically described as a minimal surface having the ring as its
only boundary. This is known to everybody. In this letter we suggest a
relativistic extension of the above fluidodynamic system where the soap film is
replaced by a Kalb-Ramond gauge potential \b(x) and the ring by a closed
string. The interaction between the \b-field and the string current excites a
new configuration of the system consisting of a relativistic membrane bounded
by the string. We call such a classical solution of the equation of motion an
axionic membrane. As a dynamical system, the axionic membrane admits a
Hamilton-Jacobi formulation which is an extension of the H-J theory of
electromagnetic strings.Comment: 15 page
Gauge Theory of Relativistic Membranes
In this paper we show that a relativistic membrane admits an equivalent
representation in terms of the Kalb-Ramond gauge field
encountered in string theory.
By `` equivalence '' we mean the following: if is a solution of the
classical equations of motion derived from the Dirac-Nambu-Goto action, then it
is always possible to find a differential form of {\it rank three}, satisfying
Maxwell-type equations. The converse proposition is also true. In the first
part of the paper, we show that a relativistic membrane, regarded as a
mechanical system, admits a Hamilton-Jacobi formulation in which the H-J
function describing a family of classical membrane histories is given by
. In the second part of the
paper, we introduce a {\it new} lagrangian of the Kalb-Ramond type which
provides a {\it first order} formulation for both open and closed membranes.
Finally, for completeness, we show that such a correspondence can be
established in the very general case of a p-brane coupled to gravity in a
spacetime of arbitrary dimensionality.Comment: 35 pages, PHYZZX, UTS-DFT-92-
Static potential from spontaneous breaking of scale symmetry
We determine the static potential for a heavy quark-antiquark pair from the
spontaneous symmetry breaking of scale invariance in a non-Abelian gauge
theory. Our calculation is done within the framework of the gauge-invariant,
path-dependent, variables formalism. The result satisfies the 't Hooft basic
criterion for achieving confinement.Comment: 13 pages, Latex, no figures; final version accepted for publication
in PLB, new references and comments, physical results unchange
Gauge procedure with gauge fields of various ranks
The standard procedure for making a global phase symmetry local involves the
introduction of a rank 1, vector field in the definition of the covariant
derivative. Here it is shown that it is possible to gauge a phase symmetry
using fields of various ranks. In contrast to other formulations of higher rank
gauge fields we begin with the coupling of the gauge field to some matter
field, and then derive the gauge invariant, field strength tensor. Some of
these gauge theories are similar to general relativity in that their covariant
derivatives involve derivatives of the rank n gauge field rather than just the
gauge field. For general relativity the covariant derivative involves the
Christoffel symbols which are written in terms of derivatives of the metric
tensor. Many (but not all) of the Lagrangians that we find for these higher
rank gauge theories lead to nonrenormalizable quantum theories which is also
similar to general relativity.Comment: References adde
Vacuum Bubbles Nucleation and Dark Matter Production through Gauge Symmetry Rearrangement
Modern particle physics and cosmology support the idea that a background of
invisible material pervades the whole universe, and identify in the cosmic
vacuum the ultimate source of matter-energy, both seen and unseen. Within the
framework of the theory of fundamental relativistic membranes, we suggest a
self-consistent, vacuum energy-driven mechanism for dark matter creation
through gauge symmetry rearrangement.Comment: 22pages, RevTeX, no figures; accepted for publication in Phys.Rev.
Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime
We discuss the relation between string quantization based on the Schild path
integral and the Nambu-Goto path integral. The equivalence between the two
approaches at the classical level is extended to the quantum level by a
saddle--point evaluation of the corresponding path integrals. A possible
relationship between M-Theory and the quantum mechanics of string loops is
pointed out. Then, within the framework of ``loop quantum mechanics'', we
confront the difficult question as to what exactly gives rise to the structure
of spacetime. We argue that the large scale properties of the string condensate
are responsible for the effective Riemannian geometry of classical spacetime.
On the other hand, near the Planck scale the condensate ``evaporates'', and
what is left behind is a ``vacuum'' characterized by an effective fractal
geometry.Comment: 19pag. ReVTeX, 1fig. Invited paper to appear in the special issue of
{\it Chaos, Solitons and Fractals} on ``Super strings, M,F,S,...Theory''
(M.S. El Naschie and C.Castro, ed
String Propagator: a Loop Space Representation
The string quantum kernel is normally written as a functional sum over the
string coordinates and the world--sheet metrics. As an alternative to this
quantum field--inspired approach, we study the closed bosonic string
propagation amplitude in the functional space of loop configurations. This
functional theory is based entirely on the Jacobi variational formulation of
quantum mechanics, {\it without the use of a lattice approximation}. The
corresponding Feynman path integral is weighed by a string action which is a
{\it reparametrization invariant} version of the Schild action. We show that
this path integral formulation is equivalent to a functional ``Schrodinger''
equation defined in loop--space. Finally, for a free string, we show that the
path integral and the functional wave equation are {\it exactly } solvable.Comment: 15 pages, no figures, ReVTeX 3.
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