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Infinitedimensional representations of the graded Lie algebra (Sp(4):4). Representation of the paraBose operators with real order of quantization

Exploring quantum non-locality with de Broglie-Bohm trajectories J. Chem. Phys. 136, 034116 (2012) Categorical Tensor Network States AIP Advances 1, 042172 (2011) The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach J. Math. Phys. 52, 072104 (2011) Quantum mechanics without an equation of motion

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation J. Chem. Phys. 137, 22A535 (2012) The spectral shift function and Levinson's theorem for quantum star graphs J. Math. Phys. 53, 082110 (2012) Explicit formulas for noncommutative deformations of PN and HN J. Math. Phys. 53, 073502 (2012) Coherent averaging in the frequency domain Following the ideas ofWigner, we quantize noncanonically a system of two nonrelativistic point particles, interacting via a harmonic potential. The center of mass phase-space variables are quantized in a canonical way, whereas the internal momentum and coordinates are assumed to satisfy relations, which are essentially different from the canonical commutation relations. As a result, the operators of the internal Hamiltonian, the relative distance, the internal momentum, and the orbital momentum commute with each other. The spectrum of these operators is finite. In particular, the distance between the constituents is preserved in time and can take at most four different values. The orbital momentum is either zero or one (in units 11/2). The operators of the coordinates do not commute with each other and, therefore, the position of anyone of the constituents cannot be localized; the particles are smeared with a certain probability in a finite space volume, which moves together with the center of mass. In the limit ~ the constituents "fall" into their center of mass and the composite system behaves as a free point particle.

In the framework of the Lagrangian field theory a new statistics for charged tensor fields is considered. An interaction Lagrangian is constructed such that the S–matrix is unitary, covariant and causal.