About DV
by
Victor Gershun
In February 1967 D.V.Volkov organized a laboratory of theoretical-group
methods on high energy physics at the department of theoretical physics under
the guidance of A.I. Akhiezer, and invited me to become a collaborator in this
laboratory.
By that time I independently investigated a possibility to
describe the masses difference between electron and 
-meson
like a superconductive solution in QED. At that time there
appeared a spontaneous 
-symmetry
breaking. This question was closely connected by DV sphere of research (symmetry
spontaneous breaking in phenomenological Lagrangian method for group spaces,
supersymmetric spaces and space factor) at that time. I did not get a positive
result of my research because of coupling between two electrons as a result
of electromagnetic interaction repulsive character impossibility, but not the
gravity, like in superconductivity model.
in 1969 DV suggested me and V. Tkach a collaboration in current
phenomenological Lagrangians structure for product Lie groups and factor groups.
In 1970 I was suggested to guide the diploma paper of the last course student
K. I suggested him the aim of multipurpose scattering in quark model for photoproduction
processes of neutral vector mesons on nucleons in vector dominance model. This
task was successfully solved at the beginning of 1971.
DV suggested me a collaboration in the possibility of phenomenological
Lagrangian writing research for anticommuting fermion fields and its consideration
as a Goldstone field. His idea was based on the analogy with spontaneously broken
symmetry. In this model the Goldstone fields were described by matrix, belonging
to 
fundamental representation.
At this time 
-mesons
belonged to 
subgroup, scalar over group Lorentz-spinor 
-mesons
belonged to 
spinor representation . DV suggested to exchange the 
group with space-time rotations group and isotopic spinors with anticommuting
spinor fields. Under this anticommuting generators were closed on rotation groups
generators. We considered various parametrization of this group, symmetric spaces
on it and space factor with rotation group as a subgroup, though constructed
phenomenological Lagrangians led to the second order degrees for fermions
instead of the first order equations. For this it was necessary to extend the
rotation group to Poincaire group and consider the rotation group in 5-dimentional
space (de Sitter group), including the translation generators over space-time
group parameters.
This idea appeared in DV a year later, but by then I decided
that the task of phenomenological Lagrangian construction for anticommuting
fermion field has no solution and accepted the suggestion of Prof. B. to apply
the idea of repeated scattering to the description of photo- and electroproduction
of nucleon resonators on kernels processes.
It should be mentioned, that at the time DV actively collaborated
with experimentators and demanded an active work from his laboratory collaborators
with various experimental groups and performing lectures in electro-magnetic
processes and strong interaction. Besides he performed several research simultaneously
with the laboratory collaborators and the students on diploma.
Having lost the stimulus to the research of Goldstone fermions
in the person of his young collaborator, he left this theme for some time.
At that time DV together with V.Akulov examined the processes
of weak interaction in participation of neutrino and the idea came to his mind,
that neutrino is the only pretender to the role of Goldstone fermion.
In 1972 he suggested V.Akulov to investigate this problem
together. And at the same time he suggested the idea the use Poincaire group
instead of rotation group together with anticommuting spinor generators. The
group, got in such a way was further called a supergroup.
And though it turned out later, that neutrino was not a Goldstone
particle, the idea of space-time coordinates extension by additional anticommuting
coordinates, connected with each other by mutual superformations, turned out
to be very fruitful. This led to the consideration of functions, depending simultaneously
on space-time coordinates and anticommuting coordinates. The degeneration of
such functions at the final measure Fourie row over anticommuting coordinates
led to the notion of superfields and supersymmetry between physical fields (even
and odd degeneration terms over supercommuting coordinates).
Translated into English by Tatiana Kudryashova