The Homological Kähler-De Rham Differential Mechanism part I : Application in General Theory of Relativity
Joint Authors
Mallios, Anastasios
Zafiris, Elias
Source
Advances in Mathematical Physics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-02
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The mechanism of differential geometric calculus is based on the fundamental notion of a connection on a module over a commutative and unital algebra of scalars defined together with the associated de Rham complex.
In this communication, we demonstrate that the dynamical mechanism of physical fields can be formulated by purely algebraic means, in terms of the homological Kähler-De Rham differential schema, constructed by connection inducing functors and their associated curvatures, independently of any background substratum.
In this context, we show explicitly that the application of this mechanism in General Relativity, instantiating the case of gravitational dynamics, is related with the absolute representability of the theory in the field of real numbers, a byproduct of which is the fixed background manifold construct of this theory.
Furthermore, the background independence of the homological differential mechanism is of particular importance for the formulation of dynamics in quantum theory, where the adherence to a fixed manifold substratum is problematic due to singularities or other topological defects.
American Psychological Association (APA)
Mallios, Anastasios& Zafiris, Elias. 2011. The Homological Kähler-De Rham Differential Mechanism part I : Application in General Theory of Relativity. Advances in Mathematical Physics،Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-453218
Modern Language Association (MLA)
Mallios, Anastasios& Zafiris, Elias. The Homological Kähler-De Rham Differential Mechanism part I : Application in General Theory of Relativity. Advances in Mathematical Physics No. 2011 (2011), pp.1-14.
https://search.emarefa.net/detail/BIM-453218
American Medical Association (AMA)
Mallios, Anastasios& Zafiris, Elias. The Homological Kähler-De Rham Differential Mechanism part I : Application in General Theory of Relativity. Advances in Mathematical Physics. 2011. Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-453218
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-453218