The XXIX International Colloquium on Group-Theoretical Methods in Physics

August 20-26, 2012, Chern Institute of Mathematics, Tianjin, China

The Wigner Medal

The Wigner Medal was established in 1977/8 and was awarded for the first time at the Integrative Conference on Group Theory and Mathematical Physics (7th International Group Theory Colloquium 1978) to Eugene P. Wigner and Valentine Bargmann. The purpose of the Wigner Medal is to recognize outstanding contributions to the understanding of physics through group theory.

The Wigner Medal is administered by the Group Theory and Fundamental Physics Foundation, a publicly supported organization. Donations are tax deductible as provided in Section 170 of the Internal Revenue code.

The Wigner Medal is awarded for "outstanding contributions to the understanding of physics through group theory." The awardee is chosen by an international selection committee whose members are elected by the Board of Trustees of the Foundation and by the Standing Committee of the International Group Theory Colloquium.

**The 2012 Wigner Medal has been awarded to Alden Mead for his seminal work on the gauge theory of the Born-Oppenheimer method for molecules and its consequences in molecular spectra and scattering. Mead discovered the underlying gauge symmetry and showed that it gives rise to both Abelian and non-Abelian gauge potentials in the effective Schr\"odinger equation for the nuclear motion in molecules. These non-local gauge potentials can significantly alter the symmetry properties of the nuclear motion wave function and must be included in order to predict the correct experimental observables. Examples include: the experimentally confirmed symmetry reversal (E<-->A) between the lowest two vibrational states of Jahn-Teller distorted X_3 molecules, and the sign change of the interference term between the reactive and non-reactive contributions to the differential cross sections in X + X_2 scattering. The theory is general and applies to any quantum system which can be decomposed into ¡°fast¡± and ¡°slow¡± degrees of freedom. Applications of this theory to other fields such as condensed matter have continued to expand with great interest to this day.
**

Wigner Medalist Conference (Poster)

Alden Mead (University of Minnesota, USA)

**Title:** Permutation Symmetry for Molecular Systems with Identical Nuclei

**Abstract:** The development of the study of degeneracy manifolds which contain symmetry manifolds as submanifolds in molecular systems of identical nuclei is reviewed, particularly with respect to the symmetry of electronic wave functions under permutations of identical nuclei. Early progress has been mainly in the systems X3 and X4, for which there are two simplifying features, viz: The number of internuclear distances is the same as the number of internal coordinates, and the deviations from degeneracy can often be described in terms of a two-dimensional irreducible representation of the relevant permutation group.

We consider the study of systems of more than four identical nuclei, concentrating on the X5 system. We show that for such system there exists no internal coordinate system that treats all identical nuclei equivalently. The problem of constructing electronic wave functions which are single-valued with respect to the nuclear coordinates is discussed, both for the integer and half-odd integer electronic spin cases.

**Time:** Thurday, August 23, 8:30 am-9:30am

**Place:** Main Lecture Hall, the second floor, Shiing-Shen Building, Nankai University

The previous recipients of the Wigner Medal are:

1978 *E. P. Wigner*

1978 *V. Bargmann*

1980 *I. M. Gel'fand*

1982 *L. Michel*

1984 *Y. Ne'eman*

1986 *F. G¨¹rsey*

1988 *I.M. Singer*

1990 *F. Iachello*

1992 *J. Wess and B. Zumino*

1996 *V. Kac and R.V. Moody*

1998 *M. Moshinsky*

2000 *L. O'Raifeartaigh*

2002 *H.J. Lipkin*

2004 *E. Inon¨¹*

2006 *S. Okubo*

2010* M. Jimbo*