Related papers: Notes on basis-independent computations with the D…
The author's idea of {\it algebraic compositeness} of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. i) For all fundamental particles of…
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…
Spontaneous mirror symmetry violation is carried out in nature as the transition between the usual left (right)-handed and the mirror right (left)-handed spaces, in each of which the usual and mirror particles have the different lifetimes.…
Using the nonrelativistic approximation in the curved-space Dirac equation, the analog of the Pauli equation is derived for a weak gravitational field with a gauge fixing condition related to the synchronous gauge, in the presence of an…
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…
We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases in which the masses are the same but Va < Vb, where V is the time-component of a vector potential. We prove generally…
Spin is a fundamental degree of freedom, whose existence was proven by Dirac for an electron by imposing the relativity to quantum mechanics, leading to the triumph to derive the Dirac equation. Spin of a photon should be linked to…
We use the $\zeta$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a…
In this paper we intend to extend some ideas of a recently proposed Lorentz-invariant Bohmian model, obeying Klein-Gordon equations, but considering particles with a spin different than zero. First we build a Bohmian model for a single…
In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac…
We prove an index formula for the Dirac operator acting on two-valued spinors on a $3$-manifold $M$ which branch along a smoothly embedded graph $\Sigma \subset M$, and with respect to a boundary condition along $\Sigma$ inspired by an…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The…
The present theory is closely related to Dirac's equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =…
In this work we describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. In more detail, using four…
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…
We consider on a spin manifold with boundary a Dirac operator $D_A$ with chiral boundary conditions, twisted by a unitary connection $A$. When $m$ is not in the chiral spectrum of $D_A$, we define an analogue of the Dirichlet-to-Neumann map…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…