Effective-Action Expansion in Perturbation Theory

Abstract

I present a systematic method for the development of the effective-action expansion in perturbation theory. The multiderivative terms beyond the effective potential can be evaluated in a direct and simple manner relying only on the familiar momentum space and Feynman propagator. I have used the self-coupled scalar field to explain the details of this new formulation. The effectiveaction expansion for this model in the one-loop approximation is evaluated up to the terms containing four derivatives. This method can be readily generalized to other models with spins and internal symmetries.It has always been an important problem in physics to extract the dominant contribution of the shortdistance effects on the large-distance behavior. A classical example is the multipole expansion. In the local relativistic quantum field theory the short-distance effects are mostly due to quantum fluctuations. In the low-energy limit, short-distance effects are not explored in detail. Typical examples are the effects of heavy particles, confining particles, and quantum fluctuation of the light particles. It is more convenient io eliminate those degrees of freedom not directly observable and incorporate their effects into an effective action of the observable fields. The expansion of this necessarily nonlocal effective action into an infinite series of local actions in the order of the number of space-time derivatives is known as the effective-action expansion.This effective-action expansion is best formulated in the functional integral method in which the unobserved fields are integrated out. The calculation of the effective potential, which is the leading term of the expansion with no derivative, is well known.

Integrating out heavy particles with functional methods: a simplified framework

“…One of the issues recently arisen involves the widely used technique to perform the functional integration set up more than thirty years ago by the works of Aitchison and Fraser [11][12][13][14], Chan [15,16], Gaillard [17] and Cheyette [18]. As implemented by refs.…”

Effective field theory of integrating out sfermions in the MSSM: Complete one-loop analysis

“…The CDE assumes in the CW potential the double derivatives (indicated by 0 ) to the beyond SM fields acting on the Lagrangian potential terms can be decomposed as V 00 ¼ M 2 þ δV 00 , where M 2 is some large constant squared mass term which is irrelevant to Higgs vacuum expectation value (VEV), and δV 00 on the other hand captures the spacetime dependent part (namely the SM Higgs) of potential terms, with not only the physical Higgs boson but the Nambu-Goldstone modes before electroweak symmetry breaking. At last ∼ generally indicates a Baker-Campbell-Hausdorff expansion with covariant derivatives and ∂ ∂p s, which can be understand as introducing spacetime dependence in the momentum space [8] (and the covariant generalization in gauge field ∂ → D ¼ ∂ − igA is given in [9,10], in which theG terms arise).…”

One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models

“…Gh, 11.15.Kc, 11.27.+d A renewed interest in the computation of quantum energies around classical configurations has recently arose. See for example [1][2][3][4][5][6][7] and references therein. The methods used to approach the problem include the derivative expanssion method [1], the scattering phase shift technique [2], the mode regularization method [4], the zeta-function regularization technique [5] and also the dimensional regularization method [7].…”

“…See for example [1][2][3][4][5][6][7] and references therein. The methods used to approach the problem include the derivative expanssion method [1], the scattering phase shift technique [2], the mode regularization method [4], the zeta-function regularization technique [5] and also the dimensional regularization method [7]. In this letter I will give a very simple derivation of the one loop renormalized soliton quantum mass correction in 1+1 dimensional scalar field theory models, using the scattering phase shift technique.…”