Real linear operators arise in a range of applications of mathematical physics. In this paper, basic properties of real linear operators are studied and their spectral theory is developed. Suitable extensions of classical operator theoretic concepts are introduced. Providing a concrete class, real linear multiplication operators are investigated and, motivated by the Beltrami equation, related ...

The algebra su 2 is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators J + and J − of the group SU 2 (with J + = J † − = HUr where H is Hermitean and Ur unitary). The Wigner-Racah algebra of SU 2 is developed in a new basis arising from the simultanenous diagonalization of the commuting operators J 2 ...

1 Schrödinger Equation and Time Development Operators 1 1.1 Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Time-dependent kets and operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Solutions to Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Time developme...

It is shown that the N = 4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is...