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Register a new userOn Verification of the Non-Generational Conjectural- Derivation of First Class constraints: HP Monopoles Field case
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K. Rasem Qandalji
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In [7] we proposed a non-generational conjectural derivation of all first class constraints (involving, only, variables compatible with canonical Poisson brackets) for realistic gauge (singular) field theories; and we verified the conjecture in cases of electromagnetic field, Yang Mills fields interacting with scalar and spinor fields, and the gravitational field. Here we will further verify our conjecture for the case of t Hooft- Polyakov (HP) monopoles field (i.e. in the Higgs Vacuum); and show that we will reproduce the results in Ref.[6], which we reached at using Diracs standard multi-generational algorithm.
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We propose a single-step non-generational conjecture of all first class constraints,(involving only variables compatible with canonical Poisson brackets), for a realistic gauge singular field theory. We verify our proposal for the free electromagnetic field, Yang-Mills fields in interaction with spinor and scalar fields, and we also verify our proposal in the case gravitational field. We show that the first class constraints which were reached at using the standard Diracs multi-generational algorithm will be reproduced using the proposed conjecture. We make no claim that our conjecture will be valid for all mathematically plausible Lagrangians; but, nevertheless the examples we consider here show that this conjecture is valid for wide range or much of realistic fields of physical interest that are know to exist and are manifested in nature
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of dispiration. Then we carry out explicitly path integration for the propagator of a particle moving in the non-Euclidean medium under the influence of a scalar potential and a vector potential. We obtain also the winding number representation of the propagator by taking the non-trivial topological structure of the medium into account. We extract the energy spectrum and the eigenfunctions from the propagator. Finally we make some remarks for special cases. Particularly, paying attention to the difference between the result of the path integration and the solution of Schrodingers equation in the case of disclination, we suggest that Schrodinger equation may have to be modified by a curvature term.
We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions.
This paper is a response to an article (R. de la Madrid, Journal of Physics A: Mathematical and General, 39,9255-9268 (2006)) recently published in Journal of Physics A: Mathematical and Theoretical. The article claims that the theory of resonances and decaying states based on certain rigged Hilbert spaces of Hardy functions is physically untenable. In this paper we show that all of the key conclusions of the cited article are the result of either the errors in mathematical reasoning or an inadequate understanding of the literature on the subject.
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