Quantising Gravity Using Physical States of a Superstring

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 the quantised operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, 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 co-derivatives. The Riemann-Christoffel affine connections are calculated and the weak field Ricci tensor R μν is shown to vanish. The interaction part R int μν is found out and the exact Rμν of the 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. By the use of a projection operator, it is shown that the gravitons are the quanta of the general relativity field which gives the Einstein equation Gμν = 0. It is suggested that quantum gravity may be renormalisable by the use of the physical ground states of the superstring theory.