Related papers: Fibre bundle formulation of nonrelativistic quantu…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
We propose a new fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
Time-dependent quantum evolution is described by an algebraic connection on a $C^\infty(R)$-module of sections of a $C^*$-algebra (or Hilbert) fibre bundle.
We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular field theory on smooth fibre bundles over a time axis.…
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this…
Some elements of classical mechanics and classical statistical mechanics are formulated in terms of fibre bundles. In the bundle approach the dynamical and distribution functions are replaced by liftings of paths in a suitably chosen…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…