We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition ...

Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator Ĵ such that A is Ĵ-Hermitian, that is, ĴA = AĴ , is found. Moreover, we construct a positive definite Hermitian Q such that A is...

We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary and sufficient conditions for the possibility of such a representation can be obtained by combining Clebsch-Gordan theory and the reciprocity theorems assoc...

2.1 Quantum stochastic calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Fock space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Weyl operators and the Bose fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Quantum stochastic integrals . . . . . . . . . . . . . . . . . . . . . . . . . ...

The κ−Poincare group and its algebra in an arbitrary basis are constructed. The κ−deformation of the Weyl group and its algebra in any dimentions and in the reference frame in which g00 = 0 are discussed.

We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the variational equation governed by a simple model Hamiltonian called the ”resonant Hamiltonian”. Three typical coherent states are considered: SU(2), SU(1,1) ...