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Geometry and physics today. (English) Zbl 1111.83019
This essay represents a kind of meta-theoretical comparison study, between different geometrization methods in theoretical physics: the old ones, belonging to classical differential geometry must (in the author’s opinion) be replaced by some new methods, in the framework of “abstract” differential geometry (described as a general gauge theory on topological manifolds and fiber bundles).

83C45Quantization of the gravitational field
81P05General and philosophical topics in quantum theory
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
Full Text: DOI
[1] Auyang, S. Y. (1995). How is Quantum Field Theory Possible? Oxford Univ. Press, Oxford.
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[3] Bergmann, P. G. (1979). Unitary Field Theory: Geometrization of Physics or Physicalization of Geometry? In ”The 1979 Berlin Einstein Symposium.” Lecture Notes in Physics, No 100. Springer-Verlag, pp. 84--88.
[4] Bogolubov, N. N., Logunov, A. A. and Todorov, I. T. (1975). Introduction to Axiomatic Quan/-tu/-m Field Theory. W.A. Benjamin, Reading, Mass.
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[11] Mallios, A. (1986). Topological Algebras. Selected Topics. North-Holland, Amsterdam. [This item is also quoted, for convenience, throughout the text, by TA].
[12] Mallios, A. (1998a). On an axiomatic treatment of differential geometry via vector sheaves. Applications. Math. Japonica (Int. Plaza) 48, 93--180. · Zbl 0910.53013
[13] Mallios, A. (1998b). Geometry of Vector Sheaves. An Axiomatic Approach to Differential Geometry, Vols. I (Chapts I--V), II (Chapts VI--XI). Kluwer, Dordrecht. [This is still quoted in the text, as VS].
[14] Mallios, A. (2002). Remarks on ”singularities.” gr-qc/0202028. · Zbl 02201337
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[17] Mallios, A. (2005). Modern Differential Geometry in Gauge Theories. Vol.I: Maxwell Fields, Vol.II: Yang-Mills Fields. Birkhäuser, Boston, (2005/2006). · Zbl 1116.18006
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[20] Mallios, A. and Raptis, I. (2003). Finitary, causal, and quantal vacuum Einstein gravity. Ibid. 42, 1479--1620. · Zbl 1033.83018
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