Strings in pp-wave background and background B-field from membrane and its symplectic quantization

TL;DR

This paper applies symplectic quantization to open membranes and strings in pp-wave backgrounds with background B-fields, revealing a noncommutative phase-space structure and offering a more elegant derivation of Poisson brackets.

Contribution

It introduces a symplectic quantization approach to derive Poisson brackets for membranes and strings in complex backgrounds, highlighting noncommutativity and improving upon previous methods.

Findings

Reproduces noncommutative phase-space structure for strings in pp-wave background.

Derives Poisson brackets among Fourier modes and coordinates.

Proposes a more elegant method for obtaining Poisson algebra.

Abstract

The symplectic quantization technique is applied to open free membrane and strings in pp-wave background and background gauge field obtained by compactifying the open membrane in the presence of a background anti-symmetric 3--form field. In both cases, first the Poisson brackets among the Fourier modes are obtained and then the Poisson brackets among the membrane(string) coordinates are computed. The full noncommutative phase-space structure is reproduced in case of strings in pp-wave background and background gauge field. We feel that this method of obtaining the Poisson algebra is more elegant than previous approaches discussed in the literature.