(1953-1997)

Nikita Alexeevich Sveshnikov, Associate Professor at the Department of Physics of Moscow State University, a brilliant scientist and educator, untimely died on July 29 1997, aged 44.

As a graduate of the Chair of Quantum Statistics in the Department of Physics of MSU, headed by Professor N.N. Bogoliubov, Nikita Sveshnikov started his scientific endeavors early in his undergraduate years. In his Diploma work and then PhD thesis under the supervision of Professor D.V. Shirkov he studied the problem of infrared divergences in Quantum Field Theory. Such divergences known since 1930s have acquired a special interest in connection with the problem of confinement of quarks in Quantum Chromodynamics. N.A. Sveshnikov was the first to realise that a consistent application of the method of asymptotic dynamics, which exactly describes interaction processes of particles at asymptotically large times, to massless models of non-Abelian symmetry may give rise to nontrivial restrictions on the spectrum of the theory. In a series of works in late 1970s - early 1980s he has shown that in a model charge symmetric theory there are no states with non-zero non-Abelian charge, and in the framework of perturbative Quantum ChromoDynamics there are no asymptotic states corresponding to free quarks, what may be interpreted as an indication for confinement. Later on during his scientific career, Nikita Alexeevich turned again to these related problems of infrared divergences, asymptotic dynamics and confinement, and continued to work on them productively to the last day of his life.

An important contribution by N.A. Sveshnikov to the Quantum Gauge Field Theory was in recognition of the special role of surface terms and delocalised observables (variables at infinity) in Quantum Gluodynamics formulated in the physical Fock-Schwinger gauge. He also developed elegant functional integration techniques for adequately taking such variables into account and studying the dependence of the partition function on the boundary conditions. This has allowed him to explain the mechanism of the confinement-deconfinement phase transition in SU(N)-gluodynamics. He has shown that below the critical temperature only the zero value of the colour charge flux in any angular cone at spatial infinity is statistically realisable. The latter is equivalent to the `no-escape' condition of colour in any angular direction and mathematically expresses the singletness of physical observables with respect to the subgroup of gauge transformations at infinity, which in turn ensures fulfillment of the Wilson confinement criterion. The numerical value for the string tension coefficient predicted by this theory is close to that from Monte Carlo lattice simulations.

These works had a natural development in later results for the theory of jet reactions at high energies obtained in mid-1990s. In particular, the connection of the main class of observables to the energy-momentum tensor was established.

It should be noteed that the supreme theoretical abilities of Nikita Alexeevich enabled him to construct consistent theories in fields which until then were only amenable to half-phenomenological treatments. The mathematical gift was perhaps one of his strongest points -- one is tempted to think of a genetic predisposition. Sometimes it might even seem that mathematics obscures the physical side for him. However, such an impression is certainly wrong -- the physics of any phenomenon was always on the forefront of his thinking.

As time went on, the scope of Nikita Alexeevich's scientific interests expanded. His extensive erudition and superlative skill allowed him to work successfully on a few pivotal theoretical problems from different branches of physics, and not physics alone, simultaneously. For example, he studied propagation of information in distributed systems. In particular, he demonstrated that a population of neurons not directly interacting with each other, but only via secreting a special chemical into their common environment and responding to local variations in its concentration, are capable of carrying out rather complex functions in transferring information. Also, more complicated systems with large organic molecules as active units and messenger-molecules carrying information about the addressee code were studied.

Sadly, untimely death interrupted the diverse scientific studies of Nikita Alexeevich. He left many unpublished or partially published results at different stages of completion, which will continue to be submitted to press by his colleagues and students. Among his late works it is interesting to mention the original study of special non-Pauli states in three-body systems, the development of the theory of quantum bound states embedded in continuum, the study of classical analogues of such states: bound states without classical turning points, and the development of methods for construction of isospectral Hamiltonians.

For Nikita Alexeevich scientific research was always inseparable from teaching. The latter was one of the most important sides of his activity. It would be no exaggeration to say that he put his heart into teaching students from the Chair of Quantum Theory and High Energy Physics in the Department of Physics of MSU, headed by Professor A.A. Logunov, and the Division of Nuclear Physics as a whole, where he was Deputy Head for many years. He liked and knew how to teach well, and his pedagogical talent matured with every year. For the current generation of students of the Department of Physics Nikita Alexeevich was one of the best loved lecturers. Anyone, who had the privilege of knowing him, will remember how rapidly Nikita Alexeevich perfected as a University teacher and researcher. This was clear to his undergraduate and postgraduate students, the number of which constantly increased. During the past few years he was giving a full-year special course on Quantum Field Theory. His contribution to the organisation of various other topical courses, such as e.g. the course `Quantum Field Theory for Experimentalists' given by Professor D.V. Shirkov, was also invaluable. Nikita Alexeevich had a striking ability to carry the weight of organisational and public duties with elegance and ease, and every job was invariably done in the most efficient and comprehensive manner.

One such duty, closely related to research and teaching, was the job into which Nikita Alexeevich put his heart during the last 12 years. In 1985 he helped organising the first Summer School for Young Scientists on Quantum Field Theory and High Energy Physics convened by the Nuclear Physics Institute of MSU. Gradually, this Summer School grew into an annual international event, widely known in Russia and worldwide as the QFTHEP Workshop. Since the first School and every year Nikita Alexeevich was the key figure in the Organising Committee. His admirable presentations and numerous discussions he organised will be long remembered by many participants of QFTHEP. As usual, he played a most active role in the preparation of the 12-th QFTHEP Workshop, which took place already after his demise in September 1997 in Samara and was dedicated to his memory.

N.A. Sveshnikov was, despite his young age, a person to whom people came for advice and opinion. His sharp wit, deep knowledge, and importantly, outgoing personality helped to many in their problems. Nikita Alexeevich was also a rather modest and self-disciplined person. He was a man of many talents, among which the art of human relations was intrinsic to him. It was no accident that he always played an important role in the social life of the Department of Physics in Moscow State University.

Nikita Alexeevich, our dear colleague and good friend, was generously blessed with many talents. The words `TALENT' and `CHARM' would perhaps characterise him best of all. It would be wrong to say that he left this life, for his accomplishments, scientific results, ideas and dreams will stay with us for ever.

Friends, colleagues and disciples will cherish the grateful memory of this remarkable man.

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V.A. Rubakov, V.I. Savrin, A.A. Slavnov,

V.I. Trukhin, O.A. Khrustalev, D.V. Shirkov

The original text of this obituary in Russian.
*UFN, No 2, 109 (1998).*

Graduated from Physics Faculty, Moscow State University (1976).

Ph.D. from Moscow State University (1981) under supervision of Professor D.V. Shirkov.

Associate Professor, Department of Quantum Theory and High Energy Physics, Physics Faculty, Moscow State University.

Research speciality: Elementary Particle Physics and Field Theory, Thermodynamics and Statistical Physics.

- Kamenschik, A.Yu., Sveshnikov N.A., Absence of free quarks in perturbative QCD. Physics Letters B, 1983, 123, No 3/4, 255-258.
- Kamenschik, A.Yu., Sveshnikov, N.A., "Quarks 84", Proc. Intern. Sem., 1985, p. 258.
- Imashev, M.S., Sveshnikov, N.A., Dynamical time formulation of quantum mechanics and the Bohr-Sommerfeld quantization rule. Preprint NPI MSU, 1987, No 87-19/96, 15 p.
- Krivchenkov, I.V., Sveshnikov, N.A., "Quarks 86", Proc. Intern. Sem., 1987, p. 339.
- Krivchenkov, I.V., Sveshnikov N.A., Asymptotics of the massive particle propagator in a model related to the Heisenberg algebra (In Russian). Teoreticheskaya i matematicheskaya fizika, 1989, 78, No 2, 215-226.
- Mikhailov, A.S., Sveshnikov, N.A., Dual description and dynamics of the Hopfield model. Preprint NPI MSU, 1989, No 50/127, 30 p.
- Sveshnikov N.A., Krivchenkov I.V., Asymptotics of massive particle propagator in a model related with Heisenberg algebra (in Russian). Theor. Math. Fiz. (1989) 78 , No 2, 154-162.
- Krivchenkov, I.V., Sveshnikov, N.A., "Problems of High Energy Physics and Field Theory", Proc. XI Workshop, 1989, p. 231.
- Mikhailov, A.S., Mitkov I.V., Sveshnikov, N.A., Molecular associative memory. BioSystems, 1990, 23, No 4, 291-295.
- Izhikevich, E.M., Mikhailov A.S., Sveshnikov, N.A., Memory, learning, and neuromediators. BioSystems, 1991, 25, No 4, 219-229.
- Mikhailov, A.S., Mitkov I.V., Sveshnikov, N.A., Associative memory with mediators. J. of Nonlinear Biology, 1991, No 2, 263-272.
- Mikhailov, A.S., Igikevich E.A.., Sveshnikov, N.A., Pattern recognition by realistic neural nets. J. of Nonlinear Biology, 1991, 4 No 1, 243-457.
- Sveshnikov N.A., Timoshenko E.G., Confinement phase transition mechanism of SU(2)-gluodynamics. Preprint IHEP, 1991, No 91-140, 30 p.
- Sveshnikov N.A., Timoshenko E.G., Confinement phase transition in gluodynamics. Preprint IHEP, 1992, No 92-31, 13 p.
- Sveshnikov, N.A., Timoshenko E.G., Confinement phase transition in gluodynamics. Physics Letters B, 1992, 289, No 3/4, 423-428.
- Sveshnikov N.A., Non-Pauli states in 3-body systems. In: "Proc. of Int. Workshop on Quantum Systems. Minsk, 23-29. V.1994, Eds. A.O.Barut et al., World Scientific, Singapore, p. 71-78 (1994).
- Sveshnikov N.A., Timoshenko E.G., Confinement phase transition in gluodynamics via variables at infinity. Problems on High Energy Physics and Quantum Field Theory - Proceedings of the XV Workshop, IHEP, Protvino, pp. 162-168 (1995).
- Sveshnikov N.A., Non-Pauli states in quantum systems. In.:"Problems on High Energy Physics and Field Theory" Proc.of XVI Workshop. IHEP, Protvino, p.198-206 (1995).
- Sveshnikov N.A., Tkachov F.V., Jets and quantum field theory. Phys. Lett B 382: (4) 403-408 AUG 15 1996.
- Sveshnikov N.A., Timoshenko E.G., The partition function versus boundary conditions and confinement in the Yang-Mills theory. Phys. Rev. D. In press. Scheduled to appear in issue D 15, 15 Oct (1998).

It is with a feeling of deep sadness and irrecoverable loss that we have heard of the untimely death of Nikita Aleexeecich. In the name of N.A. Sveshnikov Theoretical Physics has lost an extremely talented scientist, a great educator and a very nice person. No matter how big influence Nikita Alexeevich's ideas had on his students and on colleagues who knew him well, it would be only fair to say that it is for future generations to judge their true merit. It was one of N.A. Sveshnikov's gifts to be able to see farther ahead in search for the hidden mathematical beauty of the physical world, the beauty that expresses the essence of all things.

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4. N.A. Sveshnikov, E.G. Timoshenko. Boundary effects and confinement in the gauge field theory.

Collective Variables in Field-Theoretical Models.

In the last ten years I have been working on application of methods of quantum field theory, first of all the functional integration formalism, to several problems in which collective degrees of freedom play the crucial role.

One group of problems was related to construction of theoretical models of patterns recognition by neural nets. Our starting point was the remark that the action-at-a-distance principle used in Hopfield-like models is not quite satisfactory from physical viewpoint. Moreover, the number of interneural links grows in such models like (number of neurons)^2 leading to difficulties in analog modelling of them. We have proposed a model with only local interactions between "neurons" and information messengers - "neuromediators" - diffusing over the medium. The use of functional integral formulation of this model enabled us to show its equivalence in the limit of fast diffusion to the original Hopfield one. However, there is a possibility to formulate the whole dynamics of pattern recognition process in terms of neuromediator variables, the whole number of which may be done no more than the number of stable patterns in the case of point-like neurons, and only one if neurons possess different spatial structure.

Recently I was working on investigation of the longstanding problem of colour confinement in nonAbelian gauge field theories. We succeeded in constructing of a model of confinement in gluodynamics based on the Yang-Mills theory itself without additional assumptions. The crucial point was the discovery of a new type of collective variables emerging in physical gauges. Physically, the latter are variables dual to colour fluxes at spatial infinity. Mathematically, they are the so-called variables at infinity stemmed out from algebraic QFT. There is a close analogy between these quantities and the order parameters of the BCS model of superconductivity and the Higgs model. Results for the string tension and confinement phase transition temperature obtained in the framework of our model are in good agreement with lattice simulations.

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