Some Mathematical Methods of Physics

Mathematical Methods of Theoretical Physics

On some spectral problems of mathematical physics

The article contains a brief survey of some spectral problems of mathematical physics that have been arising recently in optics, mesoscopic systems, quantum chaos, and other areas. In particular, problems of photonic crystal theory, waveguides, and quantum graphs are addressed. This text is a modified version of the lectures delivered at the Pan-American Advanced Studies Institute (PASI) on Par...

Some Beautiful Equations of Mathematical Physics

The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. Dirac Lecture delivered at the I...

Cellular Automata Methods in Mathematical Physics Cellular Automata Methods in Mathematical Physics

Cellular automata (CA) are fully discrete, spatially-distributed dynamical systems which can serve as an alternative framework for mathematical descriptions of physical systems. Furthermore, they constitute intrinsically parallel models of computation which can be e ciently realized with special-purpose cellular automata machines. The basic objective of this thesis is to determine techniques fo...

Lectures on Geometric Methods in Mathematical Physics