Gauge Theory of Relativistic Membranes

Abstract

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 $F=dB=d{S}^1\wedge d{S}^2\wedge d{S}^3$. 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.

35 pages, PHYZZX, UTS-DFT-92-5

References in corpus (4)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Type II p-branes: the brane-scan revisited
• Membrane Pregeometry and the Vanishing of the Cosmological Constant
• Axionic Membranes

Cited by in corpus (21)

• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Resource Letter on geometrical results for Embeddings and Branes
• Higher Derivative Gravity and Torsion from the Geometry of C-spaces
• Quenched, Minisuperspace, Bosonic p-brane Propagator
• Hints of a New Relativity Principle from $p$-brane Quantum Mechanics
• Quantum fluctuations of a "constant" gauge field
• Bags and Confinement Governed by S.S.B. of Scale Invariance
• Weyl-Conformally-Invariant Lightlike p-Brane Theories: New Aspects in Black Hole Physics and Kaluza-Klein Dynamics
• p-Branes as Composite Antisymmetric Tensor Field Theories
• String Propagator: a Loop Space Representation
• Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime
• Conformally Invariant Gauge Theory of 3-Branes in 6D and the Cosmological Constant
• de Sitter Space Decay and Cosmological Constant Relaxation in Unimodular Gravity with Charged Membranes
• The QCD Membrane
• Weyl-Invariant Lightlike Branes and Soldering of Black Hole Space-Times
• Postmodern String Theory: Stochastic Formulation
• Lagrange Brackets and U(1) fields
• p-Branes from Generalized Yang-Mills Theory
• Two-twistor Description of Membrane
• Sphere-like Solutions in Surface Functional Theory and Dirac's Membrane Model
• Membranes and gauged supergravity