5 research outputs found
The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
We investigate an algebraic model for the quantum oscillator based upon the
Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the
algebra of supersymmetric quantum mechanics", and its Fock representation. The
model offers some freedom in the choice of a position and a momentum operator,
leading to a free model parameter gamma. Using the technique of Jacobi
matrices, we determine the spectrum of the position operator, and show that its
wavefunctions are related to Charlier polynomials C_n with parameter gamma^2.
Some properties of these wavefunctions are discussed, as well as some other
properties of the current oscillator model.Comment: Minor changes and some additional references added in version
Selfadjoint operators in spaces of functions of infinitely many variables
Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses
Perturbation determinants for singular perturbations
For proper extensions of a densely defined closed symmetric operator with trace class resolvent difference the perturbation determinant is studied in the framework of boundary triplet approach to extension theory