Is V_{eff} truly the density of effective action in QFT?

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SUMMARY

The discussion centers on the definition of the effective potential, V_{eff}, in Quantum Field Theory (QFT) and its relationship to the effective action, \Gamma_{eff}. V_{eff} is defined as \Gamma_{eff}/VT, where VT represents spacetime volume. Participants clarify that while V_{eff} can be derived from the effective action, it is specifically termed the effective potential due to its association with field interactions, such as the \Phi^4 theory. This distinction is crucial for accurate terminology in QFT.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with effective action and effective potential concepts
  • Knowledge of the \Phi^4 field theory
  • Basic grasp of spacetime volume in theoretical physics
NEXT STEPS
  • Study the derivation of effective action in Quantum Field Theory
  • Explore the implications of effective potential in \Phi^4 theory
  • Learn about the role of spacetime volume in QFT calculations
  • Investigate the differences between effective action and effective potential in various field theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, students of Quantum Field Theory, and researchers focusing on field interactions and effective actions in particle physics.

ndung200790
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Please teach me this:
Why do we not call V[itex]_{eff}[/itex]=[itex]\Gamma_{eff}[/itex]/VT (where [itex]\Gamma[/itex][itex]_{eff}[/itex] is the effective action, VT is spacetime volume) being density of effective action of field?
Thank you very much in advance.
 
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I have just known(from Schoeder's QFT book) that V[itex]_{eff}[/itex]=v[itex]_{0}[/itex]([itex]\Phi[/itex][itex]_{cl}[/itex])[itex]\Phi[/itex][itex]^{4}_{cl}[/itex].Then this must be called effective potential,because it relates with interaction Phi-4(this case is an example) but must not be called density of action.Is that correct?
 

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