Quantizing gravity using physical states of a superstring

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 a one to one correspondence with the quantized field operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, using the quantum field theory method of quantization. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantized 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 µν⁰ is shown to vanish. The interaction part R µν^int is found, and the exact R µν of the theory of gravity is expressed in terms of the quantized 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 gravitons are quanta of the general relativity field which gives the Einstein equation G µν = 0. It is suggested that quantum gravity may be renormalizable by the use of the massless ground state of this superstring theory for general relativity, and a tachyonic vacuum creates and annihilates quanta of quantized gravitational field.