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Several quantum mechanical problems are studied all of which can be approached using algebraic means. The first problem introduces a large class of Hamiltonian operators which can be related to elements of su(2) or su(1, 1) Lie algebras. A Casimir operator can be obtained and the model can be solved in general by introducing an appropriate basis. The second system involves a collection of lattice spin Hamiltonian models. It is shown how a matrix representation can be determined for these types of models with respect to a specific basis. Using these matrices secular polynomials as functions of the energy eigenvalues and their corresponding eigenvectors are calculated. The last system is similar to the first, but is suited to a particular application The eigenvectors of the model are used used to calculate the Berry phase for these states. [ABSTRACT FROM AUTHOR]

This article studies an iterative collective matching pennies (MP) quantum game, where every player interacts with his neighbours. The MP game evolves by allowing every player to adopt the strategy of his best paid mate. The behaviour in fair and unfair contests is examined. [ABSTRACT FROM AUTHOR]

We explain features of two dimensional structures in a precise way, in terms of the non-commutative space which defines these structures. The novel feature here is a fundamental explanation for the FQHE. [ABSTRACT FROM AUTHOR]

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures. [ABSTRACT FROM AUTHOR]

The movement of topological or deformable surfaces was shown to create a helicoid surface. The description of dynamics in the parametric space of helicoid introduces a new understanding to quantum mechanics and field theory. The different equations of quantum mechanics can be obtained from a general equation of motion derived from helicoidal dynamics. It was shown that space and time can be transformed into each other in parametric space. [ABSTRACT FROM AUTHOR]

The problem of developing a formalism of quantum theory, which is both consistent with the reality of the measurements and with the invariance properties of relativistic theories, is considered. A solution is found by using a real formulation of quantum mechanics, such that there exists an interpretation of the real properties of a physical system at all times. It is demonstrated also that several concepts in quantum field theory can be recast in a real formalism. [ABSTRACT FROM AUTHOR]

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime. [ABSTRACT FROM AUTHOR]