Speaker
Prof.
József Cseh
Description
Wigner did a pioneer work in the application of group theory in physics [1].
He made especially great contributions to the particle and nuclear physics [2].
The essential role of the representations of the inhomogeneous
Lorentz group in classifying the elementary particles [3] is well known:
a particle (fundamental or composite) transforms according to an
irreducible representation.
His U{ST}(4) symmetry of the spin-isospin space [4] played a very
important role in finding the classification of the nuclear states.
A direct consequence is the supermultiplet scheme of the internal
degrees of freedom. An indirect, but equally important one, is that
it served as a prototype of the dynamical symmetries,
invented later on for similar purposes.
The nucleus is a many-nucleon system, which can be described only with
simplifying models. From structural viewpoint the basic models are the
shell, the collective and the cluster models. One has to
understand, how they are related to each other, what is their common
intersection, and what kind of nature the specific states have.
In 1958 the answer was found in terms of the U(3) group [5].
This is the symmetry of a state in the real 3 dimensional space,
and togeteher with the U{ST}(4) it characterizes the wavefunction
completely. From the shell model basis this symmetry selects the
collective states of rotation [5], as well as the clusterization [6,7].
Elliott's U(3) group refers to a single major shell problem.
Later on several algebraic models (with well-defined symmetry
properties) have been invented for the description of the nuclear
structure. Based on their comparison [8] the U(3)xU(3) dynamical
symmetry seems to be appropriate for revealing their interrelations and
for classifying the nuclear states of multi-major-shell excitations.
In this contribution we discuss the similarities and the differences
of the two classification schemes: the particle and the nuclear ones.
[1] E.P. Wigner, Grouppentheorie und Ihre Anwendung auf die Quantenmechanik
der Atomspektren, Braunschweig, F. Vieweg und Sohn, 1931.
[2] E.P. Wigner, Nobel Lecture, 1963.
[3] E.P. Wigner, Ann. Math. 40, 149 (1934).
[4] E.P. Wigner, Phys. Rev. 51, 106 (1937).
[5] J.P. Elliot, Proc. Roy. Soc. A245, 128; 562 (1958).
[6] K. Wildermuth, Th. Kanellopoulos, Nucl. Phys. 7, 150 (1958).
[7] B.F. Bayman, A. Bohr, Nucl. Phys. 9, 596 (1958/59).
[8] J. Cseh, in preparation.
