Related papers: Quantum connection, charges and virtual particles
We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
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.…
We present a bundle geometric formulation of non-relativistic many-particles Quantum Mechanics. A wave function is seen to be a $\mathbb{C}$-valued cocyclic tensorial 0-form on configuration space-time seen as a principal bundle, while the…
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…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
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…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
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…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
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 discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
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…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…