Thermal Field Theory Integration over the modes?

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SUMMARY

The discussion centers on the mathematical aspect of "integration over the modes" in Thermal Field Theory, specifically the transition from the integration measure \(\int D\phi\) to \(\int D\phi_1 D\phi_2...D\phi_N\) between equations 6 and 7. Participants seek clarification on the methodology behind this transformation. The reference to a Green's function manuscript highlights the relevance of equilibrium Quantum Field Theory (QFT) in real-time formalism, providing additional context for the inquiry.

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  • Understanding of Thermal Field Theory
  • Familiarity with integration measures in functional analysis
  • Knowledge of Quantum Field Theory (QFT) principles
  • Experience with Green's functions in physics
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  • Study the derivation of integration measures in Thermal Field Theory
  • Explore the concept of functional integration in Quantum Field Theory
  • Review the real-time formalism of Quantum Field Theory
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Mathematicians, theoretical physicists, and students of Quantum Field Theory seeking to deepen their understanding of integration techniques in Thermal Field Theory.

Phymath
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The question is more of a mathematical question then one about physics in the attached file between equations 6 and 7 it says "integration over the modes" i don't know how they go from the integration measure

[tex] \int D\phi \rightarrow \int D\phi_1 D\phi_2...D\phi_N[/tex]

any advice would be helpful, thanks in advance!
 

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