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.
Read Online or Download Quantum Geometry: A Framework for Quantum General Relativity PDF
Similar differential geometry books
This publication offers the elemental notions of differential geometry, equivalent to the metric tensor, the Riemann curvature tensor, the basic types of a floor, covariant derivatives, and the basic theorem of floor conception in a self-contained and obtainable demeanour. even though the sector is usually thought of a classical one, it has lately been rejuvenated, due to the manifold functions the place it performs a vital position.
Introduces uniform structures of many of the recognized compactifications of symmetric and in the neighborhood symmetric areas, with emphasis on their geometric and topological buildings fairly self-contained reference aimed toward graduate scholars and study mathematicians drawn to the functions of Lie conception and illustration concept to research, quantity conception, algebraic geometry and algebraic topology
Multivariable research is a vital topic for mathematicians, either natural and utilized. except mathematicians, we predict that physicists, mechanical engi neers, electric engineers, platforms engineers, mathematical biologists, mathemati cal economists, and statisticians engaged in multivariate research will locate this publication tremendous beneficial.
- Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics: In Memory of Gu Chaohao
- Differential Geometry Applied to Dynamical Systems (World Scientific Series on Nonlinear Science, Series a)
- Typical dynamics of volume preserving homeomorphisms
- Differential equations on fractals: a tutorial
- Eichfeldtheorie: Eine Einführung in die Differentialgeometrie auf Faserbündeln
Extra info for Quantum Geometry: A Framework for Quantum General Relativity
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).