arXiv subjects
Publications and source records attributed to Daniel Sepunaru.
This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.
We argue that in contrast to the classical physics, the measurements in the quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant relative phases. Simultaneity is needed since in general the measurement changes the state of the system (in quantum physics and in classical physics as well). We call that measurement procedure the holographic detection. Mathematically it is described by the set of mutually commuting self adjoint operators similar and closely related to projections. We present explicit examples and discuss general features of the corresponding experimental setup which we identify as the quantum reference frame.
We present the realization of Hurwitz algebras in terms of 2x2 vector matrices, which maintain the correspondence between the geometry of the vector spaces used in the classical physics and the underlined algebraic foundation of the quantum theory. The multiplication rule used is modification of the one originally introduced by M.Zorn. We demonstrate that our multiplication is not intrinsically non-associative; the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. The extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We discuss briefly the applications of the obtained results to the extensions of the standard Hilbert space formulation of the quantum physics and to the alternative wave mechanical formulation of the classical field theory.
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).
Reformulation of Dirac equation in terms of real quadratic division algebra of quaternions is given. Similar equations with different mass term are identified as suitable for description of free propagating quark motion. The complete orthonormal set of the positive-energy plane wave solutions is presented. Therefore, Zitterbewegung phenomenon is absent in this formulation. The probability current is proportional to the momentum, as in standard Schrodinger wave mechanics.