Quantum Gravity models - brief conceptual summary

Abstract

After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions.

24 pages; invited article for the book "Mathematical Structure of the Universe", publ. Copernicus Center Press, Copernicus Center for Interdisciplinary Studies, Cracow 2014, p.277-300; v2:the text (besides added Abstract and Contents in hep version) as published in the book, with minor errors corrected, references ordered alphabetically

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