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Relativistic three-dimensional quasipotential (equal-time) equations are considered, which describe bound states of fermion and boson of spin S=0 or S=1. The spin structure of the interaction quasipotentials in such systems is studied, and…
The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase…
In the present work we recall and extend the results of previous work concerning the time evolution of open quantum systems. We show how general properties of such systems are related to their structure properties, those of their…
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular…
Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
When confined to small regions quantum systems exhibit electronic and structural properties different from their free space behavior. These properties are of interest, for example, for molecular insertion, hydrogen storage and the…
This study investigates the dynamics of fermion-antifermion pairs within a traversable wormhole spacetime by solving the two-body covariant Dirac equation with a position-dependent mass.
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a…
We extend Dirac's approach about the quantization of the electric charge to the case of gravitational configurations. The spacetime curvature is used to define a phase-like object which allows us to extract information about the behavior of…
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…
We study the quantum dynamics of conversion of composite bosons into fermionic fragment species with increasing densities of bound fermion pairs using the open quantum system approach. The Hilbert space of $N$-state-function is decomposed…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
The problem of confinement of fermions in 1+1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the…
Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic)…
The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the…