One of the most important areas of study in mathematics, physics and engineering involves scattering and the propagation of scalar and vector waves. This topic is very mathematical, which often obscures the physics and engineering of scattering and propagation. It is the goal of this author to introduce this topic in a manner where the emphasis is placed on the physical interpretations of the mathematics involved without losing the mathematical rigor. Lastly, a number of important developments in this field are discussed that have never been mentioned in books before as they are hidden...

Structured as a dialogue between a mathematician and a physicist, Symmetry and Quantum Mechanics unites the mathematical topics of this field into a compelling and physically-motivated narrative that focuses on the central role of symmetry.

Aimed at advanced undergraduate and beginning graduate students in mathematics with only a minimal background in physics, this title is also useful to physicists seeking a mathematical introduction to the subject. Part I focuses on spin, and covers such topics as Lie groups and algebras, while part II offers an account of position and...

Deformation theory is used as a tool for studying the structure of moduli schemes in geometry by many mathematicians and physicists. Mainly, the structure of the obstruction groups and their vanishing is used for smoothness properties, but there is a need to find the structure of the singularities in moduli spaces as well. This can only be achieved by constructing the singularities, and this can be done by the deformation theory studied in this book, in particular in the study of liftings by generalized matric Massey products.

This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential...