The Feynman Trajectories

Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can Be Avoided

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the absorbed particles leave on the detector is identifies as the absorption current density on the detector. This density is calculated from the solution of Schröding...

Feynman diagrams versus Fermi-gas Feynman emulator

The Feynman-Kac formula

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

The Feynman paradox revisited

We propose a simpler model in order to facilitate calculations of the Feynman paradox concerning the angular momentum of a static electromagnetic field. When an angular momentum is attached to the static electromagnetic field the paradox disappears. The storage of the angular momentum in the field during the assembling process is also analysed, It is well known that, for systems of particles sa...

THE FEYNMAN lNTEGRAL

Introduction. In 1922 Norbert Wiener [I], treating the Brownian motion of a particle, introduced a measure on the space of continuous real functions, and a corresponding integral. In 1948 Richard Feynman [2], studying the quantum mechanics of a particle, introduced a different integral over the same space. He also showed that his integral can be used to represent the solution of the initial val...