My PhD thesis was devoted to quantum fields on the Poincaré group. The topic was suggested by Dr. Andrzej Burzyński, and accepted by Dr. hab. Jan Olszewski who was my official advisor. The advisors were not very efficient in terms of publications, but they were very good at creating the right atmosphere. During that time I learned a lot of field theory and mathematical physics, from quantized Yang-Mills fields to harmonic analysis on locally compact groups. I profited from this `dowry' for many years in future.

Even the simplest interactions of quantum fields on the Poincaré group lead to nonrenormalizable models. Therefore, I began to study a promising nonperturbative approach to such models just proposed by K. Symanzik. Working with Dr. Jacek Rayski, we obtained certain results which unfortunately were discouraging. Anyway, I was disappointed by the lack of connection with real phenomena. One could explore mathematically consistent models one after another, and number of them is unlimited. My feeling was that such activity is a kind of science fiction, with the only restriction that it is formulated in mathematical terms and is mathematically correct. My interest in the fields on the Poincaré group, and generally in fields on multidimensional manifolds died away.

Soon after, in 1978, I became interested in nonabelian gauge fields. It was the period of rapid growth of QCD. I investigated mostly classical Yang-Mills fields generated by fixed external sources. This is analogous to classical electrodynamics, but much more complicated because of self-interactions of the Yang-Mills fields encoded in nonlinearity of the field equations. I think still there are issues to be clarified. I was interested also in evolution of a single particle interacting with a fixed external Yang-Mills field (classical). The particle could be the Dirac particle with bispinor wave function governed by the Dirac equation, or a classical point-like particle with spin and a nonabelian charge. The ultimate goal of these works was to understand dynamics of the system of the classical nonabelian gauge fields coupled to particles. In my opinion, it has not been achieved yet. I stoped working on these topics around 1990. Recently the subject has got a new life due to applications in theory of quark-gluon plasma.

In classical effective description of confinement, quarks and anti-quarks are connected by flux-tubes, which can be regarded as thick strings or perhaps vortices. Motivated by this picture, I investigated first the so called string with rigidity, and later relativistic vortices. In particular, I wanted to obtain an effective description of the curved vortex in the Abelian Higgs model in terms of the Nambu-Goto string with certain modifications due to curvature and thickness of the vortex. Later the project was expanded by including relativistic domain walls, and even disclination lines in nematic liquid crystals. Together with my students we investigated also excited vortices and radiation emitted from them. Generally, almost all of that was about theory of topological defects. Such theoretical investigations could be continued indefinitely because of very large number of intriguing possibilities due to infinite number of nonlinearly intercoupled degrees of freedom. There was another possibility: turning to concrete applications in many branches of condensed matter physics, atomic condensates, or in cosmology (cosmic strings and domain walls). I tried both possibilities until around 2002, when suddenly I became interested in scalar fields with V-shaped field potentials. If you wish to know why, click here. For information about this line of research see   Scalar fields with V-shaped self-interaction.

Since 2017 I am interested mainly in the Majorana field and relativistic quantum mechanics of the Majorana particle. I want to clarify certain issues which I noticed while working on the second edition of our textbook "Lectures on Classical and Quantum Theory of Fields". For details click   Quantum mechanics of the relativistic Majorana ...

Partial lists of my publications can be found in popular data bases: