By Eduard Prugovečki (auth.)

This monograph provides a assessment and research of the most mathematical, actual and epistomological problems encountered on the foundational point by means of all of the traditional formulations of relativistic quantum theories, starting from relativistic quantum mechanics and quantum box thought in Minkowski house, to many of the canonical and covariant ways to quantum gravity. it's, notwithstanding, essentially dedicated to the systematic presentation of a quantum framework intended to deal successfully with those problems by way of reconsidering the rules of those matters, studying their epistemic nature, after which constructing mathematical instruments that are particularly designed for the removing of the entire easy inconsistencies.

a delicately documented ancient survey is incorporated, and extra broad notes containing quotations from unique assets are integrated on the finish of every bankruptcy, in order that the reader may be introduced up to date with the very most modern advancements in quantum box concept in curved spacetime, quantum gravity and quantum cosmology.

The survey extra presents a backdrop opposed to which the recent foundational and mathematical principles of the current method of those topics should be introduced out in sharper aid.

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**Extra info for Quantum Geometry: A Framework for Quantum General Relativity**

**Example text**

5), in terms of which the GS quantum notion of spacetime is formulated. In the context of such geometries, quantum propagation can be viewed only as a geometro-stochastic process, whereby aspacetime exciton propagates by stochastic parallel transport along all possible (c1assical or quantumcf. Chapter 5) causal stochastic paths available to it - with the total amplitude resulting, at any given point in a quantum spacetime, from such (respectively, strongly or weakly causal) propagation being obtained by the superposition principle.

341) when it is applied to the physical world around uso 6 It is interesting to compare the attitude towards non-Euclidean geometries that prevailed during the second half of the last century with the analogous attitude towards various proposals for non-Lorentzian spacetime geometries that has been prevalent during the second half of this century. The following quotation from (Kline, 1980, p. 88) summarizes its essence: "Non-Euclidean geometry and its implications about the truth of geometry were accepted gradually by mathematicians [in the course of the last century], but not because the arguments for its applicability were strengthened in any way.

7) Hence, TxM is indeed a 4-dimensional real vector space, and the coordinates of all the vectors in it are supplied by the derivatives of the above coordinate-functions of the parameter t at points on corresponding smooth curves r. 5).