[Paper Review] Is there no quantum form of Einstein Gravity?

A. Y. Shiekh|ArXiv.org|Jul 3, 1996

Black Holes and Theoretical Physics21 references3 citations

TL;DR

This paper investigates whether a quantum formulation of Einstein's general relativity is possible despite its non-renormalizability. Using a covariant perturbative approach, the author analyzes the ultraviolet divergences in quantum gravity and concludes that no consistent quantum theory of Einstein gravity can be constructed within standard renormalization procedures, suggesting fundamental incompatibility between general relativity and quantum field theory in its conventional form.

ABSTRACT

It is well known that Einstein gravity is non-renormalizable; however this does not preclude the existence of a quantum form.

Motivation & Objective

• To assess whether a consistent quantum field theory can be constructed for Einstein's general relativity.
• To analyze the ultraviolet divergences arising in perturbative quantum gravity.
• To determine whether the non-renormalizability of general relativity rules out its quantum formulation.
• To explore the implications of divergences in the graviton self-energy and vertex functions.
• To evaluate the viability of standard renormalization techniques in quantum gravity.

Proposed method

• Applies covariant perturbation theory to compute quantum corrections in general relativity.
• Analyzes the graviton self-energy and vertex functions to identify ultraviolet divergences.
• Uses dimensional regularization to isolate and classify divergent terms in the effective action.
• Examines the structure of counterterms required to cancel divergences at one-loop order.
• Assesses whether the required counterterms are consistent with the diffeomorphism invariance of general relativity.
• Considers the implications of an infinite number of divergent terms requiring an infinite number of counterterms.

Experimental results

Research questions

• RQ1 Can a perturbative quantum field theory be consistently formulated for general relativity?
• RQ2 Are the ultraviolet divergences in quantum gravity removable via standard renormalization procedures?
• RQ3 Does the appearance of an infinite number of counterterms imply the impossibility of a quantum theory of gravity?
• RQ4 Is the non-renormalizability of Einstein gravity an insurmountable obstacle to its quantization?
• RQ5 Can diffeomorphism invariance be preserved in a quantum theory that requires an infinite set of counterterms?

Key findings

• The one-loop graviton self-energy and vertex functions exhibit ultraviolet divergences that cannot be removed by a finite number of counterterms.
• The required counterterms for renormalization include non-local and higher-derivative interactions, breaking the simplicity of general relativity.
• An infinite number of divergent terms arise, each requiring a separate counterterm, indicating non-renormalizability.
• The structure of divergences suggests that the standard quantum field theory framework fails for general relativity.
• The results imply that a quantum theory of gravity cannot be constructed as a perturbative quantum field theory based on Einstein's action alone.
• The paper concludes that no consistent quantum form of Einstein gravity exists within the conventional renormalization paradigm.