Average Action and the Renormalization Group Equations

Dec, 1989
56 pages
Published in:
  • Nucl.Phys.B 352 (1991) 529-584
  • Published: 1991
Report number:
  • DESY-89-168

Citations per year

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Abstract: (Elsevier)
We formulate an effective action Γ k for averages of fields taken within a volume of size k − d . In contrast to the block-spin approach on the lattice we work in continuous (euclidean) space, preserving all symmetries. We establish how expectation values of operators with momenta smaller than k can be computed from Γ k . The average action at different scales is related by an exact renormalization group equation. We apply these ideas to the N-component ϕ 4 theory in the spontaneously broken phase and derive the one-loop renormalization group equations for the average potential. The average potential becomes convex as k → 0.
  • phi**n model: 4
  • effective action
  • field theory: Euclidean
  • renormalization group
  • path integral
  • perturbation theory: higher-order
  • spontaneous symmetry breaking
  • field equations: nonlocal