Quenched, Minisuperspace, Bosonic p-brane Propagator

TL;DR

This paper introduces a novel approximation method combining minisuperspace and quenching to derive an exact bosonic p-brane propagator, revealing a geometric equivalence to particle motion and extending the Klein-Gordon condition.

Contribution

It presents a new approximation framework for p-brane dynamics that unifies collective and center of mass modes, leading to a generalized tension-shell condition.

Findings

Exact description of p-brane collective and center of mass dynamics.

Establishment of a geometric equivalence to particle motion.

Introduction of a generalized tension-shell condition.

Abstract

We borrow the minisuperspace approximation from Quantum Cosmology and the quenching approximation from QCD in order to derive a new form of the bosonic p-brane propagator. In this new approximation we obtain an exact description of both the collective mode deformation of the brane and the center of mass dynamics in the target spacetime. The collective mode dynamics is a generalization of string dynamics in terms of area variables. The final result is that the evolution of a p-brane in the quenched-minisuperspace approximation is formally equivalent to the effective motion of a particle in a spacetime where points as well as hypersurfaces are considered on the same footing as fundamental geometrical objects. This geometric equivalence leads us to define a new tension-shell condition that is a direct extension of the Klein-Gordon condition for material particles to the case of a physical p-brane.