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In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli's exclusion principle plays a crucial role:…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…
Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged point particles, actually, is a combination of an applied external force and of the electromagnetic radiation reaction force.…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…
In the standard model the mass of elementary particles is considered as a dynamical property emerging from their interaction with the Higgs field. We show that this assumption implies peculiar deviations from the law of universal…
Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in a Grassmann algebra with two generators. The equations of motion are explicitly…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Yet, gauge symmetries merely reflect a redundancy in the state description and…
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…