Vacuum energy for Yang-Mills fields inR d ×S1: One-loop, two-loop, and beyond

  • K. Shiraishi
  • S. Hirenzaki


The vacuum energy is calculated for Yang-Mills (YM) system defined inD dimensional space-time ofS1×R d (D=d+1), where the possibility of the YM fields to acquire the vacuum expectation values onS1 is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy inD dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution (D-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).


Elementary Particle Quantum Field Theory Approximation Method Functional Form High Dimension 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • K. Shiraishi
    • 1
  • S. Hirenzaki
    • 2
  1. 1.Department of Physics, Faculty of ScienceOchanomizu UniversityTokyoJapan
  2. 2.Department of PhysicsTokyo Metropolitan UniversityTokyoJapan

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