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

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 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 $F_{\mu\nu\rho}=\partial_{\,[\,\mu}B_{\nu\rho]}$ encountered in string theory. By `` equivalence '' we mean the following: if $x=X(\xi)$ 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 $\displaystyle{F=dB=dS^1\wedge dS^2\wedge dS^3}$. 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-

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.