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We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The progress of Particle Physics is closely linked to the progress in the understanding of the fundamental constants, like the finestructure constant, the mass of the electron or nucleon, or the electroweak mixing angle. The relation…
The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance…
Understanding the properties and physical phase of the dense strongly interacting matter present in the cores of neutron stars or created in their binary mergers remains one of the most prominent open problems in nuclear astrophysics. While…
Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordstr\"{o}m, Kerr and Kerr-Newman fields. The behavior of effective potentials in the…
We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar…
We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered…
Quantum interference is investigated within the complex quantum Hamilton-Jacobi formalism. As shown in a previous work [Phys. Rev. Lett. 102, 250401 (2009)], complex quantum trajectories display helical wrapping around stagnation tubes and…
A (nearly) perfect liquid discovered in the experements with ultrarelativistic heavy ion collisions is investigated by studying the quark ensembles with four-fermion interection as a fundamental theoretical approach. The comparative…
Some aspects of atom-field interactions in curved spacetime are reviewed. Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes, which involve the role of Hawking-Unruh and…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…