Quantum Gravity and String Theory


Towards A Moyal Quantization Program of the Membrane

Authors: Carlos Castro

A Moyal deformation quantization approach to a spherical membrane (moving in flat target backgrounds) in the light cone gauge is presented. The physical picture behind this construction relies in viewing the two spatial membrane coordinates σ1, σ2 as the two phase space variables q, p, and the temporal membrane coordinate τ as time. Solutions to the Moyal-deformed equations of motion are explicitly constructed in terms of elliptic functions. A knowledge of the Moyal-deformed light-cone membrane's Hamiltonian density H(q, p, τ ) allows to construct a timedependent Wigner function ρ(q, p, τ ) as solutions of the Moyal-Liouville equation, and from which one can obtain the expectation values of the operator < H > = Trace (ρH) that define the quantum average values of the energy density configurations of the membrane at any instant of time. It is shown how a time-dependent quartic oscillator with q4, p4, q2p2 terms plays a fundamental role in the quantum treatment of membranes and displays an important p ↔ q duality symmetry.

Comments: 15 Pages. This article has been submitted to the J. Phys. A : Math.

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Submission history

[v1] 14 Nov 2009
[v2] 17 Nov 2009

Unique-IP document downloads: 159 times

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