Physics of Noncommutative Spaces with Generalised Uncertainty Relation. Solvable Models and Coherent States

      Аннотация: Mathematically noncommutativity in space-time has revealed a new direction of the theory of quantum gravity. String theory is one of the principle candidates in this approach, which tries to unify all four fundamental interactions in a single mathematical framework. Quantum field theory in noncommutative space-time explains some of the results of string theory in certain energy limit. The aim of this research was to construct many different models in noncommutative space which satisfy the generalised uncertainty relation and therefore lead to the existence of minimal lengths, areas and volumes which are in principle also the prediction of string theory. The author has also constructed coherent states and squeezed states in this space which are effectively roots of quantum entanglement. Quality of those states have been improved further by some sophisticated techniques, which might be helpful for the understanding of qubit.

Ключевые слова: Noncommutative space-time, coherent states, PT-symmetric non-Hermitian Hamiltonian systems, q-deformed algebra, Bohmian Mechanics and Exactly Solvable models.