1993/05/06 by A. Aurilia, Euro Spallucci, E. Spallucci · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/0264-9381/10/7/004
published as Class.Quant.Grav.10:1217-1248,1993 · 35 pages, PHYZZX, UTS-DFT-92-5
arxiv created 1993/05/06 · openalex publication_date 1993/07/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A relativistic membrane is usually represented by the Dirac-Nambu-Goto action in terms of the extremal area of a three-dimensional timelike submanifold of Minkowski space. The authors show that a relativistic membrane admits an equivalent representation in terms of the Kalb-Ramond gauge field F mu nu rho = delta ( mu B nu rho ) encountered in string theory. At first glance this is somewhat surprising, since the Kalb-Ramond field is usually interpreted as the spin-0 radiation field generated by a closed string. By 'equivalence' of the two representations they 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 rank 3, satisfying Maxwell-type equations, such that, in a coordinate basis: F mu nu rho (X( xi ))=constant*X mu nu rho N-(1/3!)X alpha beta gamma X alpha beta gamma where X mu nu rho represents the tangent 3-vector to the membrane world-track. The converse proposition is also true. They 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=dS 1 V-product dS 2 V-product dS 3 where the three scalar functions S i (x) are the Clebsch potentials. They introduce a new Lagrangian of the Kalb-Ramond type which provides a first-order formulation for both open and closed membranes. The advantage of the Lagrangian approach is that it shows explicitly the correspondence between the gauge formulation of the membrane in terms of the Kalb-Ramond potential and the geometric formulation of the membrane in terms of the mechanical coordinates X mu ( xi ). Finally, for completeness, they 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.