Related papers: Quantum information aspects of noncommutative quan…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schr\"odinger equation in the absence of hidden variables. This leads inevitably to a {\it many-minds…
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles…
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…
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology.…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
The main aim of this note is to show that the formalism of multi-time equations in quantum mechanics meant to represent a manifestly Lorentz-invariant theory suffers from at least three imperfections: (1) It does not cover those physical…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…
Several aspects of the time-dependent Schrodinger equation are discussed in the context of Quantum Information Theory.
Application of the noncommutative geometry to several physical models is considered.
We consider Noncommutative Quantum Mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the…
Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature…