Free Scalar Fields

  • Mikko Laine
  • Aleksi Vuorinen
Part of the Lecture Notes in Physics book series (LNP, volume 925)


The concepts of Sect. 1 are generalized to the case of a free massive scalar field living in a d + 1 dimensional spacetime. This can be viewed as a system of infinitely many coupled harmonic oscillators. The resulting imaginary-time path integral for the partition function is expressed in Fourier representation. Matsubara sums are evaluated both in a low-temperature and a high-temperature expansion. The numerical convergence of these expansions, as well as some of their general properties, are discussed.


Dimensional regularization Euler gamma function Field theory Matsubara sum High-temperature expansion Low-temperature expansion Riemann zeta function 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mikko Laine
    • 1
  • Aleksi Vuorinen
    • 2
  1. 1.AEC, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Department of PhysicsUniversity of HelsinkiHelsinkiFinland

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