The Relative Motion of Membranes

TL;DR

This paper explores the classical and quantum dynamics of membranes, deriving a generalized motion equation and attempting quantizations to understand the universe's origins from quantum fluctuations.

Contribution

It introduces a generalized classical equation for membrane motion and explores initial quantizations to address cosmological quantum fluctuation hypotheses.

Findings

Derived a generalized membrane motion equation.

Attempted quantizations of classical membrane equations.

Discussed implications for universe origin theories.

Abstract

The relative classical motion of membranes is governed by an equation of the form D(hessian D separation)=riemann times separation times momentum. This is a generalization of the geodesic deviation equation and can be derived from a simple lagrangian. Quantum mechanically the picture is less clear. Some quantizations of the classical equations are attempted so that the question as to whether the Universe started with a quantum fluctuation can be addressed.