相关论文: Fibre bundle formulation of nonrelativistic quantu…

We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity. Three structural facts organize the framework. (i)~The photon sector of free QED is a…

In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…

Representing Z/N as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum sphere to Z/N, and call the quotient spaces Heegaard quantum lens spaces. Then we use this representation of Z/N to construct an associated…

In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…

We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories,…

A path-integral approach to quantum acoustics is developed here. In contrast to the commonly utilized particle perspective, this emerging field brings forth a long neglected but essential wave paradigm for lattice vibrations. Within the…

A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…

We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Fr\"olicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position…

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…

In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…

We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of…

Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…

The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…

A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under…

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…

We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…

The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…

Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…

Classical thermodynamics is a theory based on coarse-graining, meaning that the thermodynamic variables arise from discarding information related to the microscopic features of the system at hand. In quantum mechanics, however, where one…

In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in…