Journal ArticleDOI
A New Approach to Interacting Fields
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TLDR
In this article, a model for a description of interaction, which involves particle creation, can be given as follows:==================¯¯¯¯(1)============¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯Abstract:
A model for a description of interaction, which involves particle creation, can be given as follows:
(1)
A smooth finite-dimensional manifoldM constitutes the configuration space of some interacting system.
(2)
The concept of an interacting field is formulated in terms of two-component objects which consist of a physical and a topological field component which are ‘derived’ fromM.
(3)
Interaction is described in terms of the topological linking number of the topological field components and in terms of the intrinsic field equations.read more
Citations
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On the geometric structure underlying the eikonal equation
TL;DR: In this paper, the eikonal equation π = 1/(par. delta psi par. delta x/sup i/)/sup 2/ = n'/sup 2/, ct = 0.
References
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Significance of Electromagnetic Potentials in the Quantum Theory
Yakir Aharonov,D. Bohm +1 more
TL;DR: In this article, it was shown that there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish.
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Invariant theoretical interpretation of interaction
TL;DR: In this paper, a general rule is obtained for introducing a new field in a definite way with a definite type of interaction with the original fields by postulating the invariance of these systems under a wider group derived by replacing the parameters of the original group with a set of arbitrary functions.
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Classical physics as geometry
TL;DR: In this paper, the electromagnetic field is given by the Maxwell square root of the contracted curvature tensor tensor of Ricci and Einstein, and a detailed description in terms of the existing beautiful and highly developed mathematics of topology and harmonic vector fields is traced out in detail.
Book
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Richard H. Crowell,Ralph H. Fox +1 more
TL;DR: In this article, the authors define knots and knots polynomials, and present the notion of a knot polynomial and a group of knots, and prove the van Kampen theorem.
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The Hamilton-Cartan formalism in the calculus of variations
TL;DR: In this paper, Caratheodory, Cartan, and De Donder give an exposition of the geometry of the calculus of variations in several variables, and the main emphasis is on the Hamiltonian formalism via the use of a linear differential form studied in detail by Cartan.
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