Related papers: Dirac equation and its squared form
The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for…
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
The paper deals with nonlinear one-dimensional Dirac equation. We describe its invariants set by means of the deformed linear Dirac equation, using the fact that two ordinary differential equations are equivalent if their sets of invariants…
In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…
The instability of "physical" preaccelerative solution of the Lorentz-Dirac equation is explicitly shown
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present…
The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and…
The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some…
We derive a hydrodynamics formulation for a modified Dirac equation with a nonlinear mass term that preserves the homogeneity of the original Dirac equation. The nonlinear Dirac equation admits a symmetric split into the left and…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The…
Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few…
A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In…
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove…
We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a…
We demonstrate how to find both the color diagonal form of the squared Dirac equation in the axial color background and the transformation of the color space, which makes this equation diagonal.