Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'487'895
Articles rated: 2609

28 March 2024
 
  » arxiv » quant-ph/0312078

 Article overview


Conserved Current Densities, Localization Probabilities, and a New Global Gauge Symmetry of Klein-Gordon Fields
A. Mostafazadeh ; F. Zamani ;
Date 9 Dec 2003
Subject Quantum Physics; Mathematical Physics | quant-ph gr-qc hep-th math-ph math.MP nucl-ex
AbstractFor free Klein-Gordon fields, we construct a one-parameter family of conserved current densities $J_a^mu$, with $ain(-1,1)$, and use the latter to yield a manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. Employing a recently developed method of constructing the Hilbert space and observables for Klein-Gordon fields, we then obtain the probability current density ${cal J}_a^mu$ for the localization of a Klein-Gordon field in space. We show that in the nonrelativistic limit both $J_a^mu$ and ${cal J}_a^mu$ tend to the probability current density for the localization of a nonrelativistic free particle in space, but that unlike $J_a^mu$ the current density ${cal J}_a^mu$ is neither covariant nor conserved. Because the total probability may be obtained by integrating either of these two current densities over the whole space, the conservation of the total probability may be viewed as a consequence of the local conservation of $J_a^mu$. The latter is a manifestation of a previously unnoticed global gauge symmetry of the Klein-Gordon fields. The corresponding gauge group is U(1) if the parameter $a$ is rational. It is the multiplicative group of positive real numbers if $a$ is irrational. We also discuss an extension of our results to Klein-Gordon fields minimally coupled to an electromagnetic field.
Source arXiv, quant-ph/0312078
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica