SUPERSYMMETRY AND SUPERGRAVITY THEORY
The annotation
of the cycle of works by D.V. Volkov, directed to the competition of the Prize
named after L.D. Landau of the
During the last decade physics was enriched by a sudden direction of research, based on the use of symmetry of an unusual type, under the transformation of which bosons and fermions – the particles with various meaning of spin and statistics are mutually transformed. This new direction of research received the name supersymmetry theory, which counts hundreds of publications, it eliminated principal constraints existing in the framework of common groups for nontrivial connection of internal symmetry groups with Poincare group and enlarging the sphere of groups of symmetry application in elementary particles physics.
Touching space-time coordinates transformation, the supersymmetry theory led to the review and generalization of the main states of Einstein General Relativity theory and the construction of such variants (known under the name of gravitation), which satisfy the demands of supersymmetry. The supergravity variants, including internal symmetry, are at present the main pretenders to the role of theory, jointly describing all known interactions of elementary particles.
The supersymmetry transformations were introduced independently by two groups of Soviet theoretical physicists Y.A. Golfand and Y.P. Likhtman and D.V. Volkov and V.P. Akulov.
In the presentation to the competition of the Prize named after L.D. Landau the cycle of works include the pioneer works in supersymmetry and supergravity theory, done by D.V. Volkov in the co-authorship with his pupils V.P. Akulov and V.A. Soroka.
In the works by D.V. Volkov and V.P. Akulov, which became well-known, supersymmetry transformations were introduced with the aim of non-contradictory Goldstone particles theory construction with spin ½. In these works Minkowski 4-dimentional space-time through the introduction of additional spinor anticommuting coordinates was enlarged to more general space, i.e. superspace, and Poincare groups transformation was enlarged to supersymmetry group transformations.
It was shown, that supersymmetry spontaneous breaking was indeed accompanied by the appearance of Goldstone particles which are fermions with spin ½. The Lagrangian of interacting Goldstone fermions was constructed and low energy theorems were defined for their scattering matrices. In these works by D.V. Volkov and V.P. Akulov it was shown for the first time, that supersymmetry transformations can be nontrivially defined with internal symmetries.
The works by D.V. Volkov and V.P. Akulov included into this cycle [4, 5] are the first works in the world literature on supergravity. In these works it was shown for the first time, that to show supersymmetry transformations to be connected with common variants transformations of the general relativity theory, it is necessary to translate from global supersymmetry transformations to their local generalizations. It was shown, that gauge fields, appeared as the result of such gauge field generalization, contain gravitational field and some number (depending on the group of inner symmetry) of fields with spin 3/2 and 1. The spontaneous supersymmetry breaking was considered for the first time under the presence of gauge fields (gravitational field and field with spin 3/2) and it was shown, that such supersymmetry spontaneous breaking in accordance with the Higgs mechanism is accompanied by the mass appearance in particles with spin 3/2 and, that besides, an additional important fact appears, consisting in the appearance of cosmological term in Einstein equation.
The pioneer works on supergravity formulation in terms of curved and curved superspace were fulfilled by D.V. Volkov in the authorship with V.P. Akulov and V.A. Soroka [6, 7]. In these works the main notions of differential geometry over superspaces were formulated and, especially, which is more essential the underlying of a special class of superspace from the physical point of view was firstly shown apart from zero torsion tensor and with a defined holonomy group. These results have first and foremost importance for supergravity theory.
The review by D.V. Volkov of theoretical-group and geometrical methods of arbitrary symmetry and supersymmetry groups spontaneous breaking consideration, developed by him beginning from 1968, were included into the cycles of works. These methods comprise the basis of modern spontaneously broken symmetries description and are constantly used in literature. They are essentially used in the works of underlying cycle and comprise an integer part with it.
The list of publications by D.V.Volkov, included into the cycle of works
"Supersymmetry and supergravity theory"
1. D.V.Volkov. Phenomenologicheskiye lagranzhiany, ZChAYa, 4, 3 (1973).
2. D.V.Volkov, V.P.Akulov. O vozmozhnom universalnom vzaimodeistviyi neutrino. Pisma v ZhETF, 16, 621 (1972); D.V.Volkov, V.P.Akulov. Is the neutrino a Goldstone particle? Phys.Lett., 46B, 109, (1973)
3. V.P.Akulov, D.V.Volkov Goldstounovskiye polya so spinom polovina, TMF, 18, 39 (1974)
4. D.V.Volkov, B.A.Soroka. Effect Higgsa dlya goldstounovskih chastits so spinom ½. Pisma v ZhETF, 18, 529 (1973).
5. D.V.Volkov, B.A.Soroka. Kalibrovochniye polya dlya grup symmetrii so spinornymy parametrami, TMF, 20, 291 (1974).
6. V.P.Akulov, D.V.Volkov, V.A.Soroka. O kalibrovochnih polyah na superprostranstvach s raslichnimy gruppami golonomii. Pisma v ZhETF, 22, 396 (1975).
7. V.P.Akulov, D.V.Volkov, V.A.Soroka.