My interest is in atomic and molecular physics (theoretical chemistry, one would also say), interaction of radiation with matter (atoms, molecules, elementary charges) and the fundamental concepts. Numerous subfields are encompassed by these very general areas, and it would be greatly presumptuous of me to say that they are of equal interest to me. My choice of interesting problems within these subfields would appear somewhat random, as the saying goes: Not all those who wander are lost (J.R.R. Tolkien-The Lord of the Rings), but there is a thread that connects them.In order to see this thread I will briefly describe early evolution of my scientific carrier.

My interest for science started at an early age, in my early teens, a dreamer who tried to understand the world around us. Being a dreamer is not a sufficient condition to become a scientist, perhaps an artist, because it is necessary to combine the dreams with hard facts and a good knowledge of mathematics. As I learned functional analysis and classical physics I was soon confronted with the “uncharted field”, quantum mechanics. For me it was uncharted because at school we did not even hear the word “quantum”, let alone to learn what it is. Having got hold of an introductory text book on the subject I was struck by the fact that I could not understand a word of it. Not the math but the concepts, which were totally alien to my classical experience. Several books were consulted, but the same questions remained, which made me conclude that it was not the fault of the books but the fault of my approach. That was confirmed by a professor in physics department of the University, whom I consulted about the meaning of quantum mechanics. His answer was the same that I heard over and over again in later years in discussion with the colleagues all over the world: one should renounce pictures (read classical) and accept that only the math is the legitimate approach to analyze the physics of “small”. The secret is, so the arguments went, that the rules of classical mechanics are derived from the rules of quantum mechanics. Based on this observation it is still argued by many that in the curricula of physics one should start with quantum mechanics instead of classical. In a way these arguments were a relief for me because manipulating math is so much easier than trying to figure out pictures of the things that are analyzed. My efforts were therefore channeled towards learning the subtleties of mathematical physics, forsaking the dreamer in me. The notes on the left from the time of my high school are the proofs that provided one learns sufficient abstract math, and some functional analysis, it is relatively easy to enter the field of modern physics. One only has to learn certain basic postulates, without asking questions about their meaning.

It is no wonder that when deciding on the subject of study the choice was elementary particle physics. This is even nowadays a challenge for an adventurous mind because the subject is plagued by intriguing questions, which would definitely awaken a mind of a dreamer. Furthermore, the belief was, and still is, perpetuated, primarily by high energy physicists, that the only true challenge to the physical principles comes from the field of elementary particle physics and the rest is the “stamp collecting”. My physics student days were spent in learning, besides the obligatory courses, the subtleties of mathematical formalism of high energy physics, being proud to be a member of the selected ones. That nobody could understand what I was doing, except my “club-members”, I considered more of a virtue rather than the drawback. My diploma thesis was on the weak interactions, which at that time was the “in subject”, being at the threshold of developments that resulted in the unification of three major interactions. For the thesis I calculated the radiative corrections to the muon decay, a major exercise. One of the pages of that calculation is shown in the right figure.

The diploma work was the crown of my “love affair” with high energy physics, of which I was, and still am, very proud because lots of solitary hours were spent to acquire knowledge of the field. One page of that work is in the left figure. I should have felt grand fulfillment being at the threshold of graduation, because I was ready to start contributing novelty into the field rather than reading and redoing somebody else work. Yet I felt emptiness because part of me was not involved in all these, the dreamer. I had knowledge of the facts, and especially the math, but there were lots of questions unanswered, those who one might characterize as “questions you always wanted to ask but were afraid to do so”. That part of me prevailed when after graduation I got offer for PhD in theoretical chemistry, at Sussex University. The decision was not simple, because it was the step from the privileged club to “stamp collecting”. In the end my instinct made decision, and never regretted. Those questions where the thread that connects (almost) all problems that I worked, and still working, on.

The Questions (at least some of them):

Although one accepts dualism as the fundamental principle of matter, it is hard to acquiesce with it. The question is not of acceptance but of fundamental logic: if the dualism is allowed then one should also allow trialism, quadrilism, etc., depending on what suits ones premises. I cannot see the use of similar logic in, say, the criminal law. Nevertheless, if this is the fact of Nature then so be it, but based on this principle it is hard to describe certain phenomena. One of them is tunneling. I spent fruitless hours watching waves on the surface of water in order observe something that would resemble tunneling. Electromagnetic waves show analogous effect (total internal reflection), but it could be given relatively simple meaning (the field instead of being a plane wave transforms into a decaying one). Furthermore, it was not clear to me how to reconcile manifestation on the screen of the particle property with that of wave property to describe the interference experiment. Explanation by the collapse of the wave function, which is the modern way of treating this phenomenon, pushes physics into mysticism (this and other explanations of the same kind are used as the basis for numerous mystic societies that awoke ghosts at midnight sessions - brows the internet for their locations). The effect of similar kind is the EPR paradox, which in all frankness I did not understand then and now. If one says that initial total momentum of two particles is zero, and the momentum of one is measured then by the conservation law the other is known, no matter where the two particles are located. That was the most primitive observation of mine; later a more sophisticated one was given. A very famous is the Aharon-Bohm effect, which my student seminar was, supporting it very anxiously, but eventually I admitted to myself that I did not understand it. I did not have prejudice to support either the concept of force or potential, yet I could not figure out how is it possible that one effects dynamics of particle and the other does not.

Anyone starting the course in quantum mechanics is given the answer to the basic question: what makes an atom, say hydrogen, stable. In the standard scenario it is said that classical mechanics does not explain stability because of the effect of the radiation reaction force on trajectory of the electrons. On the other hand, quantum mechanics predicts stability because the electrons have the lowest energy state. Now, this comparison is truly unfair, because in classical mechanics one assumes radiation reaction force whilst in the quantum one does not. Classical atom without that force is also perfectly stable. The proof that quantum mechanics does not predict stability of atoms is the positronium, for which one easily calculates the ground state (and in fact it is observed) but it does not have infinite lifetime. The orthodox elementary particle physicist would shrug off this argument with nonchalant ease by saying that the positronium consists of particle and antiparticle, and therefore they annihilate. However, the argument does not explain anything, because the logic is twisted. The antiparticle is defined as the one that annihilates with its counterpart particle, but there is no physical explanation how and why this happens. So the question why, for example, hydrogen atoms is stable whilst positronium is not is a mystery.
That opens a question of the nature of annihilation, but in my opinion a more important one is about creation of particles. Again, the answer that solves (nearly) everything is that the effects are not surprising because of the relationship between mass and energy, the rest mass of particles goes into the energy of the photons and vice verse. The answer is far from being satisfactory, because the relationship is the energy balance and not the mechanism how this happens. And the latter is precisely physics and the former is math. The mystery is that we are used so much on thinking that the rest mass of particles is a universal constant, and yet in the annihilation it vanishes at the expense of the radiation field (photons, if one prefers it). And what about the reverse process, would it be fantastic to know the actual physics behind the annihilation/creation processes?

One of the postulates of physics, “whose source is deeply buried in the relativistic quantum world”, is the relationship between spin of the particles and the statistics they obey. The use of this relationship is enormous; it is the basis of quantum chemistry, the theoretical description of the chemical Universe. Yet, its physical source is a mystery, which is why it is a postulate. The question is whether such a physical source exists, and what is the basis of it. The commutation/anti-commutation rules for the quantum fields are definitely not it. After all, interactions among the objects in the Universe determine the symmetries and not math, or humans who invented symmetries.

“The most accurate theory of all times” is how quantum electrodynamics is characterized. To a great extent this is true, but it is presumptions to give it this absolute status. Nevertheless, its foundations give it the status of a truly mathematical theory, which would confirm anyone learning its basics. It has no recourse to anything that is labeled as classical experience, not even quantum. The classical field and the wave function become abstract mathematical objects with certain rules to manipulate with them. Yet in the end the results are very good, “the proof of the pudding is in the eating” as a pragmatics would say. Is this sufficient to give the QED the status of physical theory? That question puzzled me greatly, because, for example, annihilation cross for the electron and the positron is calculated very accurately from the formalism that is based solely upon calculation of certain matrix elements. In this derivation there is absolutely no hint about the physics of this process. Why such an abstract theory gives good results? ; “That is the question”.

A beauty in Nature is decay of the neutron. There is a particle, an essential constituent of matter, but when left alone it splits into fragments. A classical mind would immediately start thinking about a model of the neutron, say an orbiting system, but indeed there would be problems with it. The hurdle may not be insurmountable, I am not aware that somebody spent long hours thinking of such a model, instead pragmatism prevailed. At the time when the theoreticians start thinking about rationalizing the decay of the neutron the QED was well established. In its foundations are the creation and the annihilation operators, a beautiful way to avoid any nasty questions about the nature of these processes, which were gauged specifically for the need of three particles: electron, positron and photon. Why not define the same operators for the other particles, and use the same logic for them as in the QED? Indeed that what it was done, but the problems arose. New particles had to be postulated: neutron, proton and (anti) neutrino. However, with the simple vector current in the QED it was not possible to reproduce the experimental data and so a general linear combination of interactions was assumed that would do that. In the end the famous V-A current was selected with a coupling constant that had a value not resembling anything known at that time. Its value was much smaller than the coupling constant for strong interactions (read nuclear forces) or electromagnetic interaction (of course in the dimensionless units). The constant was fit to the experimental value for the lifetime of the neutron. Because of its unique value the fourth force of Nature was introduced, but its role was only to regulate the decay of unstable particles. That description of the fourth force (week force) was puzzle for me because one is accustomed to think of interactions as regulating the whole process of encounters of particles, and not only one of its segments, the decay. The same as saying that tunneling should be treated as separate interaction because it gives rise to decay. Much later, when I learned more about atomic and molecular physics, I had a comment inphysics today about this point. Based on this abstract thinking the whole subject of modern elementary particle physics is built upon. A useful trick was used, however. Whenever there was disagreement with the experimental facts it was not the V-A idea that was questioned. Instead the theory was expended by more and more terms and parameters, when eventually the electromagnetic interactions could be also incorporated. No wonder that was possible because the basic mathematical formalism sprung from that of the QED. One only needed sufficiently large number of terms and parameters that would describe both interactions in a unified fashion.

Resonances are very intriguing “objects”, which are either observed as decaying states or a feature in the cross sections. Decaying states were known long before the concept of resonances was established, they were manifested as the instability (radioactivity) of nuclei. Rationale was given in terms of a simple model; rearrangement of energy in a many particle system (as the nuclei are), a process similar to dissociative cooling (evaporative cooling of a cup of tea), but no quantitative results came out of the model. Eventually quantum mechanics developed sufficiently to produce a different model, the decay is due tunneling. Based on this model it was possible to give better insight into the nature of strong (nuclear) interaction. The effect of tunneling gives rise to another effect, the resonances, which are manifested in the cross sections if the decaying partners are made to scatter (crudely speaking). Resonances are characterized by a well defined energy and the energy width of their impact on the cross section. A great theorem of quantum mechanics then says that this energy width is simply related to the decay rate of the unstable species. That connection is then used to understand the decay of elementary particles, and also to discover new ones. That there are elementary particles (meaning that they are not composed of more elementary species, the picture that prevailed at the time of my undergraduate study) which undergo a transformation into the other similar species was a great discovery; typical example is decay of the neutron. Few more followed, but with a much shorter lifetime (muon, pion) nevertheless sufficiently long lived to leave a trace in a detector. However, based on the relationship between resonances and decaying states a mechanism was found to discover a much more numerous family of elementary particles, with such a short lifetime that they do not leave a trace in detector but they are observed as an effect on the cross sections. Importance of resonances is unquestionable, sufficiently so to study its true origins and answer few questions of great importance. One is: should we treat short lived species the elementary particles or manifestation of the character of interaction among few basic elementary particles? What about the other model for decaying species, the dissociative cooling? It was unduly neglected in all the considerations, one reason being that it is much more difficult to analyze than tunneling (it is a many body effect) because, for example, perturbation theory would almost certainly fail.

Those questions sprung from my experience in the high energy physics, and for many of them I found the answer/understanding in atomic and molecular physics. It is not that I can now give the answer to the problems of the elementary particles, but as the saying “I seek not the answer but to understand the question” goes (citation taken from the wall of a friend of mine Harry (Kroto) ) I have better insight into them. It was precisely because of mine belief that many fundamental problems should be analyzed from the interdisciplinary point, I initiated the Brijuni conferences.