An Ultralocal Classical and Quantum Gravity Theory

TL;DR

This paper demonstrates that ultralocal classical and quantum gravity theories can be successfully quantized using affine quantization, suggesting potential for consistent quantization of Einstein's gravity with restored derivatives.

Contribution

It shows that ultralocal gravity can be quantized via affine quantization, supporting the idea that classical theories can be successfully quantized after restoring derivatives.

Findings

Ultralocal scalar fields can be quantized by affine methods.

Ultralocal gravity can be successfully quantized using affine quantization.

Restoring derivatives in ultralocal theories may lead to successful quantization of classical gravity.

Abstract

An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general relativity, by Pilati, as an initial term in a perturbation series that aimed to restore all omitted derivatives. Previously, the author has quantized ultralocal scalar fields by affine quantization to show that these non-renormalizanle theories can be correctly quantized by affine quantization; the story of such scalar models is discussed in this paper. The present paper will also show that ultralocal gravity can be successfully quantized by affine quantization. The purpose of this study is that a successful affine quantization of any ultralocal field problem implies that, with properly restored derivatives, the classical theory can, in principle, be guaranteed a successful result using either a canonical quantization or an affine quantization. In particular, Einstein's gravity requires an affine quantization, and it will be successful.