Related papers: Geometric Phase in Quaternionic Quantum Mechanics
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
We discuss gauge symmetry breaking in a general framework of gauge theories on an interval. We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements. It is shown…
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…