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The action-angle variables for the massless relativistic string in 1 + 1 dimensions

Söderberg, B. LU ; Andersson, Bo LU and Gustafson, Gösta LU (1985) In Journal of Mathematical Physics 26(1). p.112-123
Abstract

In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space-and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the... (More)

In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space-and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the Poincaré generators and the physical interpretation. For the light-cone frame variables the equivalence to a set of indistinguishable oscillators is shown, for which an excitation corresponds to an instantaneous momentum transfer to an endpoint of the string. © 1985 American Institute of Physics.

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organization
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type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
26
issue
1
pages
12 pages
publisher
American Institute of Physics
external identifiers
  • scopus:36549100691
ISSN
0022-2488
DOI
10.1063/1.526790
language
English
LU publication?
yes
id
6c3bcd20-c876-47a9-94d6-a0a6e7e99b4e
date added to LUP
2016-10-03 19:30:34
date last changed
2017-01-03 09:55:36
@article{6c3bcd20-c876-47a9-94d6-a0a6e7e99b4e,
  abstract     = {<p>In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space-and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the Poincaré generators and the physical interpretation. For the light-cone frame variables the equivalence to a set of indistinguishable oscillators is shown, for which an excitation corresponds to an instantaneous momentum transfer to an endpoint of the string. © 1985 American Institute of Physics.</p>},
  author       = {Söderberg, B. and Andersson, Bo and Gustafson, Gösta},
  issn         = {0022-2488},
  language     = {eng},
  number       = {1},
  pages        = {112--123},
  publisher    = {American Institute of Physics},
  series       = {Journal of Mathematical Physics},
  title        = {The action-angle variables for the massless relativistic string in 1 + 1 dimensions},
  url          = {http://dx.doi.org/10.1063/1.526790},
  volume       = {26},
  year         = {1985},
}