Wave function of string and membrane and spacetime geometry

TL;DR

This paper develops a first-quantized wave function framework for strings and membranes, deriving fundamental equations and spacetime properties, offering a new perspective on string and membrane theories.

Contribution

It introduces a wave function approach to string and membrane theories, connecting them to quantum equations and spacetime structure in a novel way.

Findings

Derived Klein-Gordon and Dirac equations from the wave function

Established relations between string/membrane properties and spacetime

Provided a new first-quantized framework for string and membrane theories

Abstract

A first-quantized string (and membrane) theory is developed here by using a general wave function of the string (and membrane), analogously to the first-quantized quantum theory of a point particle. From the general wave function of the string (and membrane), the properties of the string (and membrane) such as its relation to Bosons, Fermions and spacetime are investigated. The string and membrane wave functions are found to be very useful and we can deduce Klein-Gordon equation, Dirac equation and the fundamental property of the spacetime from this new starting point.