In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday
Dr. Volodymyr Tretyak is a wellknown
 Ukrainian scientist working in
 the field of theoretical physics.
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| Опубліковано в: : | Condensed Matter Physics |
|---|---|
| Дата: | 2005 |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2005
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/119657 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday // Condensed Matter Physics. — 2005. — Т. 8, № 2(42). — С. 447-450. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860260039348977664 |
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| citation_txt | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday // Condensed Matter Physics. — 2005. — Т. 8, № 2(42). — С. 447-450. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | Dr. Volodymyr Tretyak is a wellknown
Ukrainian scientist working in
the field of theoretical physics.
|
| first_indexed | 2025-12-07T18:54:02Z |
| format | Article |
| fulltext |
Editorial
In honour of doctor Volodymyr Tretyak on the
occasion of his 50th birthday
Dr. Volodymyr Tretyak is a well-
known Ukrainian scientist working in
the field of theoretical physics.
Volodymyr Ivanovych Tretyak was
born on April 24, 1955, in Lviv. In 1972
he entered the Physics department of
the Ivan Franko Lviv State Universi-
ty and specialized at the Theoretical
Physics chair. There he got the taste
for theoretical and mathematical studies
under the beneficial influence of brilliant
teachers [1]. Volodymyr Tretyak was a
constant participant of the seminars of
the eminent Ukrainian physicist Roman
Gaida [2] devoted to the problems of rel-
ativistic physics.
After graduating from the University
in 1977 V.Tretyak worked as a teacher
of physics at school in Lviv region for a year. His scientific activities started in
1978 at the Institute for Applied Problems of Mechanics and Mathematics. There
Tretyak joined the research team in relativistic mechanics founded by Roman Gaida.
(Since May, 1981 as a junior research fellow). First, under the guidance of Professor
Gaida, and then, in collaboration with him, with Yurij Kluchkovsky and with other
scientists, Tretyak took up non-traditional (especially, at the beginning of 80th) field
of theoretical physics. This is the so-called “relativistic direct interaction theory”
(RDIT). The theory describes relativistic systems of interacting particles without
using the notion of field as mediator of interaction [3]. The main achievement of the
group was the construction of three-dimensional Lagrangian formulation of RDIT.
Volodymyr Tretyak quickly swiches on to this work and studies group-theoretical
aspects of the formalism. The results were published in the four frequently cited
works [4] in 1980’s.
On this firm ground Tretyak develops the Dirac’s idea of forms of relativistic
dynamics. In 1950 Dirac proposed to construct the relativistic Hamiltonian dynamics
of particle system using some spacelike (or lightlike) hypersurface as a configuration
space [5]. This program was never accomplished by Dirac in view of its complexity.
447
Later on various solutions to this program were proposed by other theoreticians but
the physical meaning of all these results was unclear.
The young researcher considers this problem in great generality and perspective.
First of all Tretyak formulates a mathematically rigorous definition of particle config-
uration space as a disjoint union of arbitrary space- or light-like hypersurfaces. Then
he constructs the realization of a Lie group on this space by means of Lie-Bäcklung
transformations and hence studies its properties. Tretyak determines the structure
of Poincaré-invariant Lagrangians and conserved quantities in an arbitrary form of
relativistic dynamics. Moreover, he reveals the relations between different forms of
dynamics and proves their equivalence. Finally, Tretyak proposes the subsequent
approximation scheme for the transition to the canonical formalism which, actually,
completes the Dirac’s program and eliminates most of controversial questions. This
work made a Ph. D. thesis [6] defended at the famous Serpukhov Institute for High
Energy Physics in 1982.
In 1988 Tretyak joined Institute for Condensed Matter Physics of National
Academy of Sciences of Ukraine with a position of a senior research fellow. He be-
comes a councelor to young physicists. Being inclined to a mathematical grace and
rigorous results, Volodymyr Tretyak looks for new schemes providing an exact rela-
tivistic description of particle system. Tretyak lavishly shares his ideas with his fol-
lowers. As a result he and his young colleague Volodymyr Shpytko built a number of
interesting exactly solvable 2- and N -particle relativistic models in two-dimensional
front form of dynamics. Shpytko quantized them in his Ph. D. thesis [7,8]. He al-
so proposed a solvable extension of two-dimensional front form in four-dimensional
space-time, the “isotropic” form of dynamics, which was developed together with
Askold Duviryak [8].
Another collection of works is devoted to relativistic generalization of centre-
of-mass variables. The relativistic generalization of CM-variables was pursued by
Professor Gajda. Tretyak’s idea was to use such variables in the Lagrangian for-
malism in order to simplify not only a solution but the formulation of the N -body
problem itself. Using a special representation of the Poincaré group Gaida, Tretyak
and Yaremko constructed the relativistic CM-variables [9]. In these terms infinite
series for Lagrangian and Hamiltonian functions convert into compact expressions,
and a motion of N -particle system as a whole separates from internal motion of
its constituents. Using these results Yurij Yaremko solved the relativistic two-body
problem in his Ph. D. thesis in 1995 [10].
Volodymyr Tretyak defended the Doctor of Science thesis [11] in 1996. He stated
the exact structure of Lagrangians of particles interacting by means of classical
relativistic fields of arbitrary mass and spin. The guideline leading from the classical
field theory towards the relativistic particle dynamics was a surprising union of the
formalism of Fokker action integrals and the Schwinger theory of sources. Another
bridge between classical electrodynamics and the relativistic Hamiltonian dynamics
of charged particles was built by Tretyak and his post-graduate student Andrij
Nazarenko by means of Dirac’s constrained formalism. In their works [12] they got
a number of interesting results, including an exact expression for partition function
448
of the relativistic system of interacting charged particles.
Many of physical ideas by Tretyak are self-sufficient and shaped in perfect math-
ematical form. His articles are splendidly concise and his lectures give listeners a
great pleasure.
Tretyak’s scientific activities, besides research, involve membership in Shevchenko
Scientific Society and Ukrainian Physical Society. He participates in the editori-
al boards of “Journal of Physical Studies” and “Collected Physical Papers” of
Shevchenko Scientific Society. Volodymyr Tretyak is a member of the Specialized
Scientific Council at the Institute for Condensed Matter Physics of the National
Academy of Sciences of Ukraine.
Friends and Editorial Board of “Condensed Matter Physics” wish the jubilleer
and his family to stay in good health and to enjoy many happy years of life. The
colleagues hope for Dr. Tretyak’s new ideas and creative work.
References
1. Vakarchuk I.O., Hil’ H.B., Visnyk Lvivskogo Universytetu, 1992, 25, 3–13,
(in Ukrainian); In honour of Professor Ihor Yukhnovskii on the occasion of his 75th
birthday. Condensed Matter Physics, 2000, 8, No. 3(23), 697–708.
2. In Memory of Roman Gaida (1928–1998). Condens. Matter Phys., 1998, 1, No. 3(15),
417–423.
3. Hoyle F., Narlikar J.V. Action-at-a-Distance in Physics and Cosmology. Freeman,
San Francisco, 1974; Llosa J. ed. Relativistic Action at a Distance: Classical and
Quantum Aspects. – In Proc. Workshop, Barcelona, 1981, Lectures Notes in Physics,
No. 162, Berlin, Springer, 1982.
4. Gaida R.P., Tretyak V.I., Single-time form of the Fokker-type relativistic dynamics.
Acta Phys. Pol. B, 1980, 11, No. 7, 502–522; Tretyak V.I., Gaida R.P., Symmetries
and conservation laws in the single-time form of the Fokker-type relativistic dynamics.
Ibid, 523–536; Gaida R.P., Kluchkovsky Yu.B., Tretyak V.I., Lagrangian classical rel-
ativistic mechanics of a system of directly interacting particles. Teor. Mat. Fiz. 1980,
44, No. 2, 194–208; 45, No. 2, 180–198.
5. Dirac P.A.M., Forms of relativistic dynamics. Rev. Mod. Phys., 1949, 21, 392–399.
6. Tretyak V.I. Classical relativistic description of particle direct interactions in an arbi-
trary form of Lagrangian dynamics. Ph. D. Thesis, Serpukhov, 1982.
7. Shpytko V.Ye. Quantum-mechanical models of relativistic direct interaction of system
of N bodies in the front form of dynamics. Ph. D. Thesis, Lviv, 1997; Shpytko V.Ye.,
Exactly integrable model of relativistic N -body system in the two-dimensional variant
of the front form of dynamics. Acta Phys. Pol. B, 1996, 27, No. 9, 2057–2070; Tretyak
V., Shpytko V., Time-asymmetric Fokker-type action and relativistic wave equations.
J. Phys. A, 2000, 33, 5719–5738.
8. Duviryak A., Shpytko V., Tretyak V., Isotropic forms of dynamics in the relativistic
direct interacting theory. Condens. Matter Phys., 1998, 1, No. 1(15), 463–512.
9. Gaida R.P., Tretyak V.I., Yaremko Yu.G., Center-of-mass variables in the relativistic
Lagrangian dynamics of a system of particles. Teor. Mat. Fiz. 1994, 101, No. 3, 402–
416; Gaida R., Tretyak V., Yaremko Yu., Quasi-relativistic center-of-mass variables in
applications. Condens. Matter Phys., 1998, 1, No. 1(15), 425–437.
449
10. Yaremko Yu. Center-of-mass variables in relativistic Lagrangian mechanics of direct
interacting particle systems. Ph. D. Thesis, Lviv, 1995.
11. Tretyak V.I. Fokker-type action integrals and forms of relativistic Lagrangian dynam-
ics. Thesis . . . of doctor of physical and mathematical sci. Lviv, 1996.
12. Nazarenko A., Tretyak V., Classical relativistic systems of charged particles in the
front form of dynamics and the Liouville equation. Condens. Matter Phys., 2000, 3,
No. 1(21), 5–22; Duviryak A., Nazarenko A., Tretyak V., Classical relativistic system
of N charges. Hamiltonian description, forms of dynamics, and partition function.
Condens. Matter Phys., 2001, 4, No. 1(25), 5–14.
450
|
| id | nasplib_isofts_kiev_ua-123456789-119657 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T18:54:02Z |
| publishDate | 2005 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | 2017-06-07T19:07:46Z 2017-06-07T19:07:46Z 2005 In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday // Condensed Matter Physics. — 2005. — Т. 8, № 2(42). — С. 447-450. — Бібліогр.: 12 назв. — англ. 1607-324X https://nasplib.isofts.kiev.ua/handle/123456789/119657 Dr. Volodymyr Tretyak is a wellknown
 Ukrainian scientist working in
 the field of theoretical physics. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Editorial In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday Article published earlier |
| spellingShingle | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday Editorial |
| title | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday |
| title_full | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday |
| title_fullStr | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday |
| title_full_unstemmed | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday |
| title_short | In honour of doctor Volodymyr Tretyak on the occasion of his 50th birthday |
| title_sort | in honour of doctor volodymyr tretyak on the occasion of his 50th birthday |
| topic | Editorial |
| topic_facet | Editorial |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119657 |