Quantum gravity: general introduction and recent developments

Abstract

PACS 04.60.-m I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics, loop quantum gravity). I then address quantum gravitational aspects of string theory. This is followed by a discussion of black holes and quantum cosmology. I end with some remarks on the observational status of quantum gravity.

Rationale for a correlated worldline theory of quantum gravity

“…Efforts to quantize Einstein gravity go back to the 1930s [58]; the field has repeatedly been reviewed [35,[59][60][61][62][63][64]. By 'conventional' quantum gravity we will mean here a theory that starts from a generating functional…”

LQG for the Bewildered

“…We 2 Of course the choice diag(+1, −1, −1, −1) is equally valid but we will have occasion later to restrict our attention to the spacial part of the metric, in which case a positive (spatial) line-element is cleaner to work with. 3 Strictly speaking it is a pseudo-metric, as the distance it measures between two distinct points can be zero.…”

“…Accordingly we have attempted to create a discussion which we would have wanted to read when first encountering LQG. Everyone's learning style is different, and accordingly we make note of several other reviews of this subject [1,2,3,4,5,6,7,8,9,10,11], which the reader may refer to in order to gain a broader understanding, and to sample the various points of view held by researchers in the field.…”

Universal Coefficient Theorem and Quantum Field Theory

“…Quantization of gravity is probably the best example where lifting the ideas that defined quantum mechanics to a situation where the space-time has itself quantum properties became rather difficult to be done meaningfully [174]. There were several reasons and explanations for why we did not succeed in this area but, apart of all excuses, the main reason is that we do not know how to speak meaningfully about the quantum, topological and geometrical properties of the underlying manifold on which we construct our theory.…”

“…It must be said that the problems do not appear when the gravitational field is weak. We can speak meaningfully about quantum field theories on curved space-times and hence "combine quantum mechanics and gravity" [174][175][176][177][178][179][180].…”