相关论文: Quantum Configuration and Phase Spaces: Finsler an…
In this work we propose an alternative description of the quantum mechanics of a massive and spinning free particle in anti-de~Sitter spacetime, using a phase space rather than a spacetime representation. The regularizing character of the…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Finsler geometry is a well known generalization of Riemannian geometry which allows to account for a possibly non trivial structure of the space of configurations of relativistic particles. We here establish a link between Finsler geometry…
It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…