preprints.org > physical sciences > particle and field physics > doi: 10.20944/preprints202306.0258.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 2 June 2023 / Approved: 5 June 2023 / Online: 5 June 2023 (07:55:10 CEST)
Version 2 : Received: 23 June 2023 / Approved: 25 June 2023 / Online: 25 June 2023 (02:49:16 CEST)
Version 3 : Received: 17 August 2023 / Approved: 17 August 2023 / Online: 17 August 2023 (08:03:53 CEST)

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the same formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors.Thus, a unified way to describe bosons and fermions in spinor space is proposed. The consequences of the Dirac equation for the electron spinor are considered and the existence of a similar first-order equation for the photon spinor is assumed. Each spinor by means of a uniform formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field vectors, coordinates and momentum of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.The presented approach, in the long run, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

quantum field theory; Minkowski space; electromagnetic potential calibration; Lorentz force; Casimir operators; wave equation; Dirac equation

Physical Sciences, Particle and Field Physics

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