Personal webpage of George Savvidy

Research

Vacuum polarization by the intense gauge fields [1-8].Extension of the Heisenberg and Euler result in QED to non-Abelian Yang-Mills theories and prediction of the gauge boson condensation [2], essentially non-Abelian infrared phenomena. Exact solution of renormalization group equations for the effective Lagrangian in Abelian and non-Abelian gauge theories in terms of beta function and corresponding expression for the intensity of the non-Abelian gauge boson condensate.
Nonintegrability and dynamical stochastisity of the non-Abelian fields [9,14-16,18-21,28,29]. Nonlinear plane waves in pure Yang-Mills theory and notion of Y-M classical and quantum mechanics. Application of the ergodic theory to the problem of integrability of classical Yang-Mills equations.
Quantization of relativistic membrane in the light-cone gauge [31,32], analogy with Yang-Mills classical mechanics[34-36, 39]. Notion of self-dual membrane[33].
QCD string dynamics [40-44]. Feynman integral over the paths was extended to an integral over the surfaces, so that they coincide at long time scale. The action of the theory is linear and is proportional to the linear size of the surface. The string tension is generated dynamically by quantum fluctuations.
Statistical physics [45,48]. A class of Ising spin systems was introduced, the partition function of which generates random surfaces with linear action. Geometrical nature of the system allows to perform the duality transformation and to find out a new class of gauge spin systems [49,50,51]. They are in the same relation as 3D Ising ferromagnet and 3D-gauge spin systems.
Astrophysics. N-body problem [22,23]. By means of the Maupertuis principle reduction of the N-body problem to the study of the behavior of the geodesic flow on a Reimannian manifold. Negativity of the corresponding curvature and exponential instability of the geodesic trajectories. Computation of the relaxation time for the stellar systems like galaxies and globular clusters. That time is substantially smaller than binary, Chandrasekhar relaxation time.
Computational mathematics [26,27,30,47]. Application of Kolmogorov-Anosov-Sinai K-systems to the generation of pseudo-random numbers for the Monte-Karlo simulations of physical systems and it's concrete realization. The MIXMAX generator: i) it has the best discrepancy, ii) can be used for Monte-Carlo simulations in very high-dimensional spaces, by increasing the dimension of the K-system which can be taken equal or greater than the dimensionality of these spaces, iii) it is a fast generator, in the current implementation the computational complexity is of order O(N).

Talks: