Quantum gravity and "singularities"


It is our aim in the present article to point out that the phenomenal disagreement of the classical differential geometry (CDG, viz. differential geometry of smooth manifolds), when applied in the quantum domain (quantum field theory, for instance) is just due to the entanglement in that procedure of the underlying C^∈fty (:smooth)-manifold, hence, the appearance of the so-called "singularities", while the inherent, quite algebraic, in character, differential-geometric mechanism of the same classical theory still remains intact, without having to resort to any carrier space at all (!), supporting that mechanism, as it was the case, so far. Therefore, a potential application of the same, even in the quantum regime.

DOI Code: 10.1285/i15900932v25n2p57

Keywords: Quantum gravity; Singularities; Relativistic quantum mechanics; Abstract differential geometry (ADG); "Physical geometry"; Vector sheaf; Yang-Mills field; ADG-formalism; Second quantization; Einstein's equation (in vacuo); Yang-Mills equation; Sheaf cohomology

Classification: 81T05; 81T13; 81T70; 58D29; 46N50; 83C47; 83C45; 83C05

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