Quantising Gravity Using Physical States of a Superstring

TL;DR

This paper proposes a novel approach to quantum gravity by constructing a symmetric tensor from superstring modes, showing it satisfies physical constraints, and deriving the gravitational field equations within a quantised framework.

Contribution

It introduces a method to quantise gravity using superstring physical states, linking them to the metric tensor and deriving the gravitational field equations.

Findings

The constructed tensor satisfies superstring physical state constraints.

The quantum gravitational field's self-energy vanishes in vacuum.

The approach suggests quantum gravity may be renormalisable using superstring ground states.

Abstract

A symmetric zero mass tensor of rank two is constructed using the superstring modes of excitation which satisfies the physical state constraints of a superstring. These states have one to one correspondence with quantised operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensors using the Gupta-Bleuler method of quantisation. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantised field is deduced. The gravitational interaction is switched on by going over from ordinary derivatives to coderivatives.The Riemann-Christoffel affine connections are calculated and the weak field Ricci tensor $R^{0}_{\mu \nu}$ is shown to vanish. The interaction part $R^{int}_{\mu \nu}$ is found out and the exact $R_{\mu \nu}$ of theory of gravity is expressed in terms of the quantised metric. The quantum mechanical self energy of the gravitational field, in vacuum, is shown to vanish. It is suggested that quantum gravity may be renormalisable by the use of the physical ground states of the superstring theory.