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Register a new userValid for Much of Realistic Fields: A Non-Generational Conjecture For Deriving All First-Class Constraints at Once
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Authors
K. Rasem Qandalji
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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
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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.
We derive an adiabatic theory for a stochastic differential equation, $ varepsilon, mathrm{d} X(s) = L_1(s) X(s), mathrm{d} s + sqrt{varepsilon} L_2(s) X(s) , mathrm{d} B_s, $ under a condition that instantaneous stationary states of $L_1(s)$ are also stationary states of $L_2(s)$. We use our results to derive the full statistics of tunneling for a driven stochastic Schr{o}dinger equation describing a dephasing process.
It was recently shown [2] that the resolvent algebra of a non-relativistic Bose field determines a gauge invariant (particle number preserving) kinematical algebra of observables which is stable under the automorphic action of a large family of interacting dynamics involving pair potentials. In the present article, this observable algebra is extended to a field algebra by adding to it isometries, which transform as tensors under gauge transformations and induce particle number changing morphisms of the observables. Different morphisms are linked by intertwiners in the observable algebra. It is shown that such intertwiners also induce time translations of the morphisms. As a consequence, the field algebra is stable under the automorphic action of the interacting dynamics as well. These results establish a concrete C*-algebraic framework for interacting non-relativistic Bose systems in infinite space. It provides an adequate basis for studies of long range phenomena, such as phase transitions, stability properties of equilibrium states, condensates, and the breakdown of symmetries.
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $kappa$ in the case of spin and pseudospin symmetry, respectively. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method.
Electric resistance in conducting media is related to heat (or entropy) production in presence of electric fields. In this paper, by using Arakis relative entropy for states, we mathematically define and analyze the heat production of free fermions within external potentials. More precisely, we investigate the heat production of the non-autonomous C*-dynamical system obtained from the fermionic second quantization of a discrete Schrodinger operator with bounded static potential in presence of an electric field that is time- and space-dependent. It is a first preliminary step towards a mathematical description of transport properties of fermions from thermal considerations. This program will be carried out in several papers. The regime of small and slowly varying in space electric fields is important in this context, and is studied the present paper. We use tree-decay bounds of the $n$-point, $nin 2mathbb{N}$, correlations of the many-fermion system to analyze this regime. We verify below the 1st law of thermodynamics for the system under consideration. The latter implies, for systems doing no work, that the heat produced by the electromagnetic field is exactly the increase of the internal energy resulting from the modification of the (infinite volume) state of the fermion system. The identification of heat production with an energy increment is, among other things, technically convenient. We initially focus our study on non-interacting (or free) fermions, but our approach will be later applied to weakly interacting fermions.
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