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This paper reports on our diagrammatic approach to characterize the gauge dependence of Quantum Electrodynamics in the linear covariant gauge. Our dimensionally independent technique is purely based on a perturbative analysis and allows us…
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
It is shown a complex function $\Phi$ defined to be the product of a real Gaussian function and a complex Dirac delta function satisfies the Cauchy-Riemann equations. It is also shown these harmonic $\Phi$-functions can be included in the…
An alternative representation of the kernel of the evolution operator in quantum electrodynamics is obtained in the form of a functional integral, in which the gauge momentum corresponding to the Gaussian constraint is excluded from the…
In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field $F$ is expressed in terms of \QTR{em}{the observer dependent} relative vectors $\QTR{bf}{E}$ and $\QTR{bf}{B.}$ In this paper we present \QTR{em}{the…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
The work contains a detailed investigation of free neutral (Hermitian) or charged (non-Hermitian) scalar fields and the describing them (system of) Klein-Gordon equation(s) in momentum picture of motion. A form of the field equation(s) in…
We argue that the definition of the thermodynamic work done on a charged particle by a time-dependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gauge-invariant. The solution of this problem demands…
We show that if we start with the free Dirac Lagrangian, and demand local phase invariance, assuming the total phase coming from two independent contributions associated with the charge and mass degrees of freedom of charged Dirac…
We develop a non-relativistic quantum field theory of electrons and nuclei based on the Coulomb Hamiltonian. We derive the exact equations of motion and write these equations in the form of Hedin's equations for all species of identical…
We carry out the canonical quantization of the electromagnetic field in arbitrary $\xi$-gauge and compute its propagator. In this way we fill a gap in the literature and clarify some existing confusion about Feynman $i\epsilon$ prescription…
The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, $\mathsf{U}(1)$ gauge theory minimally coupled to a Dirac fermion. We construct the braided…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
The gauge field theory of the standard electroweak model in the presence of the electroweak bubble wall is investigated with a view to its applications to microscopic phenomena, which are believed to have occurred during the phase…
A gauge field treatment of a current, oscillating at a fixed frequency, of interacting neutral atoms leads to a set of matter-wave duals to Maxwell's equations for the electromagnetic field. In contrast to electromagnetics, the velocity of…
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a…