Hamiltonian formulation of the D-brane action and the light-cone Hamiltonian

TL;DR

This paper develops a Hamiltonian formulation for the bosonic D-brane action, explicitly separates constraints, imposes gauge conditions, and derives a quadratic light-cone Hamiltonian with simplified brackets.

Contribution

It introduces a Hamiltonian framework for the bosonic D-brane action, explicitly separates constraints, and derives a quadratic light-cone Hamiltonian with simplified Dirac brackets.

Findings

Explicit separation of first and second class constraints.

Derivation of a quadratic light-cone Hamiltonian.

Simplification of brackets to Poisson brackets.

Abstract

We present the Hamiltonian formulation of the bosonic Dirichlet p-brane action. We rewrite the recently proposed quadratic D-brane action in terms of generalized shift vector and lapse function. The first class and the second class constraints are explicitly separated for the bosonic case. We then impose the gauge conditions in such a way that only time-independent gauge transformations are left. In this gauge we obtain the light-cone Hamiltonian which is quadratic in the field momenta of scalar and vector fields. The constraints are explicitly solved to eliminate part of the canonical variables. The Dirac brackets between the remaining variables are computed and shown to be equal to simple Poisson brackets.