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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Classical Mechanics and Classical Fields

J. Math. Phys. 53, 022901 (2012); http://dx.doi.org/10.1063/1.3682651 (31 pages)

Classical group field theory

Joseph Ben Geloun

Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5, Canada and International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072B.P.50, Cotonou, Republic of Benin

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(Received 15 July 2011; accepted 14 January 2012; published online 9 February 2012)

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and then, on more involved nonlocal theories (colored and noncolored) defined over a tensor product of the same group, we address the issue of translation and dilatation symmetries and the corresponding Noether theorem. The energy momentum tensor and dilatation current are derived and their properties identified for each case.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE DYNAMICAL BOULATOV-OOGURI MODEL
  3. TRANSLATIONS AND DILATATIONS: 1 D GFT
    1. Translations and EMT
    2. Dilatations and current vector
  4. TRANSLATIONS AND DILATATIONS: 3 D CASE
    1. Translations and EMT
    2. Dilatations and current tensor
  5. TRANSLATIONS AND DILATATIONS: COLORED GFT
    1. Translations and EMT
    2. Dilatations and current tensor
  6. SUMMARY AND OUTLOOK

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KEYWORDS and PACS

Keywords

classical field theory, SU(2) theory

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682651

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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