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Propagation and Energy Transfer
Published in James D. Taylor, Introduction to Ultra-Wideband Radar Systems, 2020
Robert Roussel-Dupré, Terence W. Barrett
The gauge theory representation of polarization modulation based on local internal symmetry can be related to the representation of the global representation of spaces, i.e., to topology. The motivation in doing so is to provide insight into EM emitter design. The requirement, in the case of the SU(2) electromagnetic field, would be for a configuration permitting two types of closed paths: one for internal and one for external space. The torus exactly describes such a topology which represents a multiply connected (as opposed to infinitely connected) space.
All About Wave Equations
Published in Bahman Zohuri, Patrick J. McDaniel, Electrical Brain Stimulation for the Treatment of Neurological Disorders, 2019
Bahman Zohuri, Patrick J. McDaniel
As we have learned so far, in classical electrodynamics, the vector and scalar potentials conveniently were introduced by utilizing Maxwell’s Equations as an aid for calculating these fields and from there we managed to analysis them in the quantum electrodynamics via the Lagrangian and Hamiltonian aspect of gauge theory and its invariance postulation. See Chapter Five of this book for more details. However, it is a known fact that in order, to obtain a classical canonical formalism the potentials are needed. Nevertheless, the fundamental equation of motion can always be described directly in terms of the fields alone.
The classical theory of light colors: a paradigm for description of particle interactions
Published in Maricel Agop, Ioan Merches, Operational Procedures Describing Physical Systems, 2018
But the implications of a theory that uses a Resnikoff”s representation of colors, whereby they are quantitatively described by the entries of a 2 × 2 symmetric real matrix, are far more intricate from physical theoretical point of view. Indeed, such a representation has an outstanding theoretical meaning. A matrix is obviously an element of a noncommutative algebra, which can be simply a Yang-Mills field. It turns out that this classical theory of colors is plainly a Yang-Mills theory. It completes the classical theory of light in a natural way, by including the color in it. The classical electromagnetic theory, even though undoubtedly a gauge theory, is not a Yang-Mills theory yet. The present work shows that it takes considerations of color of light in order to render to the theory of light a plain Yang-Mills character. The modern “technicolor” for instance, should be a genuine classical concept. From this point of view, the light itself actually enters the realm of quantum chromodynamics, as it should naturally do, for the everyday color is related to light. But there is more to it: if the mechanism of color is the one explaining the strong interactions, then this color should be classical too. Thus one might figure out why the noncommutativity is the essential ingredient allowing asymptotic freedom in the case of strong interactions: after all, the light is a model of interaction everywhere in the universe, at any level! For more details see [34].
QED treatment of linear elastic waves in asymmetric environments
Published in Waves in Random and Complex Media, 2021
Maysam Yousefian, Mehrdad Farhoudi
In this regard, to achieve an asymmetric elastodynamic model based on the QED as a gauge theory with quantum aspects, we have generalized and then have modified the CT. During this process, first by adding vibrational degrees of freedom for microstructures in the CT and using some mathematical methods, we have achieved a covariant form of the CT. Then, while using the gauge property of the waves of displacement and also modeling fermions, by means of the Cosserat elasticity,3 we have modified the CT in a way that the resulted asymmetric elastodynamic model being fully comparable to QED. Finally, we have made a comparison between the experimental observations and the predictions of the proposed asymmetric elastodynamic model.
Sign-changing solutions for the nonlinear Chern–Simons–Schrödinger equations
Published in Applicable Analysis, 2020
Jackiw and Pi in [1,2] introduced a nonrelativistic model that the nonlinear Schrödinger dynamics is coupled with the Chern–Simons gauge terms as follows: Here, i denotes the imaginary unit, , , for , is a complex scalar filed, is the gauge filed and is the covariant derivative for κ running over 0,1,2, and is a constant representing the strength of interaction potential. The Chern–Simons gauge theory describes the nonrelativistic thermodynamic behavior of large number of particles in an electromagnetic field. This feature of the model is important for the study of the high temperature superconductor, Aharovnov–Bohm scattering and the fractional quantum Hall effect.
General Relativistic Modification of the Lockheed Compact Fusion Reactor Concept
Published in Fusion Science and Technology, 2020
This approach ignores that the gravitational field, like the electric field, should have an energy and by should have a mass. It was believed, even by Einstein, that for this reason if gravitational waves exist, they should have a mass. The resolution of this controversy came with the experimental observation of gravitational waves. Prior to his experimental verification, Hund made a convincing argument2 that in a noninertial reference system and by Mach’s principle, the inertial forces in accelerated reference systems must have sources different from the sources in Newton’s law of gravity and can be negative, as in a static gravitational field, or positive, as the mass of a gravitational wave. For this reason, the author proposed the vacuum of space is a kind of plasma made up from positive and negative Planck masses,3 which may be called a Planck mass plasma, very much like a solid is made up of positive and negative electrical charges. Even though Einstein’s gravitational field equation is unaffected by this Planck mass plasma conjecture, it obtains a deeper meaning as a non-Abelian gauge theory, as proposed by Dehnen and Ghaboussi.4