In the World of Physics: Research by Rockenbauer on Extended Dirac Equation for Elementary Fermions

Antal Rockenbauer is Professor Emeritus at the Hungarian Academy of Sciences. He published his research on the “Extended Dirac Equation for Elementary Fermions based on Applying 8-Dimensional Spinors”.  DOI: 10.13140/RG.2.2.23994.90569

In his work, the Dirac equation was extended by applying 8-dimensional spinors for the decomposition of the square root in the covariant equation of special relativity.  Subsequently, he developed a consequent quantum theory by rendering operators for the charge and rest mass.

It was found that these operators commuted with the Hamiltonian of electron and positron in the electromagnetic field. However, on observation, it was seen that they did not commute for neutrino and quarks. For neutrino, the expectation values of mass and charge were zero, which permitted these particles to advance with the speed of light.

Rockenbauer noticed that the momentum of neutrino commutes with the Hamiltonian rendering distinct values for the three types of neutrinos. This fact explains why the neutrinos could oscillate.

On further examination, it was noticed that for quarks neither the mass nor the charge operators commuted with the Hamiltonian. However, he found out, “fractional charge and renormalized mass could be considered as expectation values of the operators”.

According to Rockenbauer, measurements should have given eigenvalues of the charge operator and since that did not happen, no fractional charge could be detected excluding the possibility of observation of free quarks.

Rockenbauer assessed that such a distinction would have been of significance when one spoke about the questions why free quarks could not be observed or how the neutrinos could oscillate, as electromagnetic interaction only existed under the above conditions and no weak or strong interaction.

Rockenbauer has further explained the relativistic Dirac equation and how it gave a perfect description of the electromagnetic properties of an electron in his study.

After an in-depth study by Rockenbauer, he suggested a decomposition of the square root by putting into application eight-dimensional spinors. This not only offered operators for charge and rest mass but also lead to an extended and elaborate definition for momentum.

During the course of the study, the other conundrum of particle physics was to explain why no free quarks could be detected. Rockenbauer felt that the aforementioned problems added more fuel to the usefulness of a study especially when no weak and strong interactions are considered for the neutrinos and quarks.

He inferred that for the neutrinos the weak interaction played a role only in the creation and annihilation process. However, it was seen that when the oscillation did take place, at that instant only electromagnetic interactions could have been present. 

It was seen that for the quarks the major probe was why no free quarks could exist, and this question has been taken forward in the study conducted by Rockenbauer.

Rockenbauer has clarified that the conclusions of this paper refers to only single particles in non-bonded states.

Rockenbauer concluded his research by mentioning that the consequent relativistic quantum mechanics could give an explanation as to why the neutrino oscillation could take place even when the particles had zero rest mass. He has also described why free quarks could not be discerned with fractional charges. 

The study deduced that the neutrino oscillation and confinement of quarks divulge the presence of a conceptual significance in the development of general fermion equation. In addition to the above, a conclusion was drawn that the fractional charge of a particle could be attributed to the strong interaction between two or three quarks, whereas the zero charge and rest mass for neutrinos was brought about by the weak interaction in the transformation processes of fermions.

Rockenbauer shares that a multi-particle theory based on the strong and weak interaction can in all probability describe the quantum states where these properties mentioned are given as expectation values of the charge and rest mass operators.

Rockenbauer’s brilliant paper on the extended dirac equation for elementary fermions is a great contribution in the sphere of physics. Many physicists can look up to his research work and further contribute in the study taken up by him.

About:

Antal Rockenbauer was born on 6 July, 1938 in Budapest, graduated in 1962 in the Roland Eotvos University, Budapest, at the Faculty of Physics. He obtained PhD degree in 1965, DSC degree of the Hungarian Academy of Sciences in 1985 and habilitated in 1997. He is scientific advisor and professor emeritus in the Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences. He is private docent in the Department of Physics, Budapest University of Technology and Economic, as well as in the Roland Eotvos University. He was awarded by the title of doctor honoris causa in 2007 by the Université de Provence. He is involved in various international cooperation (Université de Provence, Aix-Marseille; Tianjin Medical University, China; The Ohio State University, Columbus, USA) His work is focused on applications of ESR spectroscopy studying structure and dynamics of free radicals and transition metal complexes. He also studied magnetic properties of high Tc superconductors and nanostructures, and applied spin labeling for biologic materials. He developed two dimensional simulation procedures for interpreting ESR spectra. He also deals with theoretical questions of relativistic quantum mechanics and particle physics. He published 300 scientific papers cited around 4,500 times.

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