Path integrals with a periodic constraint: Entangled strings
01 Nov 1978-Journal of Mathematical Physics (American Institute of Physics)-Vol. 19, Iss: 11, pp 2318-2323
TL;DR: In this paper, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates and applications are made for the entangled polymers with and without interactions, the Aharonov-Bohm effect and the angular momentum projection of a spinning top.
Abstract: Path integrals with a periodic constraint ∫θ ds =Θ+2πn (n=integer) are studied. In particular, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates. Applications are made for the entangled polymers with and without interactions, the Aharonov–Bohm effect, and the angular momentum projection of a spinning top.
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01 Jan 1965
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
Abstract: Au sommaire : 1.The fundamental concepts of quantum mechanics ; 2.The quantum-mechanical law of motion ; 3.Developing the concepts with special examples ; 4.The schrodinger description of quantum mechanics ; 5.Measurements and operators ; 6.The perturbation method in quantum mechanics ; 7.Transition elements ; 8.Harmonic oscillators ; 9.Quantum electrodynamics ; 10.Statistical mechanics ; 11.The variational method ; 12.Other problems in probability.
8,141 citations
TL;DR: In this article, it was shown that there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish.
Abstract: In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.
5,553 citations
TL;DR: In this paper, the authors formulated non-relativistic quantum mechanics in a different way and showed that the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way.
Abstract: Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function ψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.
3,678 citations
1,460 citations