Relativistic membranes

Abstract

The classical dynamics of M-dimensional extended objects arising from stationary points of the world volume swept out in space time is discussed from various points of view. A introduction to the Hamiltonian mechanics of bosonic compact M(em)branes is given, emphasing the diversity of the different formulations and gauge choices. For moving hypersurfaces, a graph description—including its nonlinear realization of Lorentz invariance—and hydrodynamic formulations (in light-cone coordinates as well as when choosing the time coordinate of a Lorentz observer as the dependent variable) are presented. A matrix regularization for M = 2 (existing for all topologies) is explained in detail for the 2-sphere, as well as multilinear formulations for M > 2. The recently found dynamical symmetry that exists for all M and related reconstruction algebras are covered, just as some explicit solutions of the level-set equations.

Singularities of relativistic membranes

“…Let us consider the motion of an M-dimensional extended object in Minkowski space R M+1,1 sweeping out an M + 1 dimensional manifold parametrized by u = (u 0 , u), cp [6]. Stationary points of the world volume…”

Supermembrane limit of Yang-Mills theory

“…See[8,9] for historical reviews and more references 2. The direct product structure is not necessary for the application of the adiabatic method.…”

Optimized Fock space in the large N limit of quartic interactions in matrix models

“…(5.22) Table 4: Comparison of the exact value of the spectral gap ω(g) [13] with the perturbative expansion in the optimized Fock space ω (0) =ω, ω (1) , ω (2) , ω (3) . Let us repeat the calculation for the MMM.…”

“…Let us consider the classical internal energy of the bosonic membrane, which in a light-cone description in orthonormal gauge can be written as (for more details see e.g. [1])…”