Professor George Savvidy is well known for his work on the non-Abelian gauge theory, in particular, on the calculation of the effective action in one loop approximation and of its exact form in all orders of perturbation theory by means of renormalization group. This development leads to the discovery of the "Savvidy vacuum" of the Yang-Mills theory, a candidate ground state whereby gluons condense into a state with energy lower than the Fock vacuum. This work is being widely cited http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+AU+SAVVIDY+AND+DATE+1977+and+journal+Phys.Lett&FORMAT=www&SEQUENCE=.

Prof. Savvidy is currently working on an extension of non-Abelian gauge field theory, formulated by Yang-Mills in 1954, to a gauge theory, which includes non-Abelian tensor gauge fields. In so extended gauge field theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrarily large integer spins. The corresponding invariant Lagrangian does not contain higher order derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant. The extended gauge theory has the same index of divergences of its Feynman diagrams as the Yang-Mills theory does and most probably will be renormalizable. The proposed extension leads to a natural inclusion of the standard theory of fundamental forces into a larger theory in which standard vector gauge bosons, leptons and quarks represent a low-spin subgroup of an enlarged family of particles with higher spins.

The above field-theoretical approach to the extension of gauge field theory to non-Abelian tensor gauge fields was inspired by another area of research which is connected with high energy behaviour of string amplitudes, the so called limit of tensionless strings. Prof. Savvidy has proposed and developed the geometrical approach in which the area action of standard string theory is replaced by a "perimeter" action, which is based on the integral of extrinsic curvature (trace of the second fundamental form). The perimeter action is "tensionless" by construction and allows to employ methods of integral geometry, including the results of Chern, for example, to obtain bounds on convergence of the corresponding partition function. Ultimately this approach led to the discovery of the extended Virasoro algebra with an extra infinite-dimensional abelian symmetry from which the above-mentioned work on non-Abelian tensor gauge field theory arose.

Prof. Savvidy for many years is giving lectures on string theory, employing the operator formalism throughout, which makes for the most immediate way of understanding the subject for both physicists and mathematicians. These lectures have been delivered at a number of universities over the years, and have been perfected in material and presentation.