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The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers will be constructed. Conditions for identifying the convolution product of groupoid functions and the star--product arising from a quantization--dequantization scheme will be given. A tomographic approach to construct quasi--distributions out of suitable immersions of groupoids into Hilbert spaces will be formulated and, finally, intertwining kernels for such generalized symplectic tomograms will be evaluated explicitly.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of sepa
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields allows us
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigners approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called gen
This paper presents the momentum map structures which emerge in the dynamics of mixed states. Both quantum and classical mechanics are shown to possess analogous momentum map pairs. In the quantum setting, the right leg of the pair identifies the Ber
Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $eta$ operators. We show that despite th