Effective Action and Loop Expansion: General Formulation

2021 ◽  
pp. 5-9
Author(s):  
Albert Petrov
Keyword(s):  
Effective Action ◽  
Loop Expansion

MESON-DIQUARK LOOP EXPANSION

1993 ◽  
Vol 08 (02) ◽  
pp. 277-300 ◽  
Author(s):  
M. LUTZ ◽  
J. PRASCHIFKA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Auxiliary Field ◽  
Quantum Field ◽  
Field Approach ◽  
Loop Expansion ◽  
Quark Models

We consider a general (nonlocal) four-fermion quantum field theory and show how the Cornwall-Jackiw-Tomboulis effective action can be systematically expanded in the number, η, of composite, bose loops. This is achieved by the introduction of auxiliary, bilocal fields which describe fermion-fermion and fermion-antifermion correlations. The η expansion can be understood as a generalization of the [Formula: see text] expansion and is of particular interest in quark models, for example, where the bilocal fields can be identified with meson and diquark degrees of freedom. Comparison with the usual loop (ħ) expansion reveals some unusual characteristics of the η expansion and throws light on recent studies of diquark degrees of freedom in which the auxiliary field approach is used.

scholarly journals Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Scale Dependence ◽  
Classical Action ◽  
Loop Expansion ◽  
Background Field Method

We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for anO(N)symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.

scholarly journals TWO-LOOP WORLDSHEET EFFECTIVE ACTION

2003 ◽  
Vol 18 (39) ◽  
pp. 2817-2828 ◽  
Author(s):  
A. R. FAZIO ◽  
G. K. SAVVIDY
Keyword(s):  
String Theory ◽  
Effective Action ◽  
String Tension ◽  
Second Order ◽  
Quantum Corrections ◽  
Loop Correction ◽  
Classical Level ◽  
Loop Expansion

We are studying quantum corrections in the earlier proposed string theory based on worldsheet action which measures the linear sizes of the surfaces. At classical level the string tension is equal to zero and as it was demonstrated in the previous studies one loop correction to the classical worldsheet action generates Nambu–Goto area term, that is nonzero string tension. We extend this analysis computing the worldsheet effective action in the second order of the loop expansion. We are studying quantum corrections in the earlier proposed string theory based on worldsheet action which measures the perimeter of the surface. At the classical level the string tension is equal to zero and we demonstrate that one and two-loop corrections to the classical worldsheet action generates Nambu–Goto area term, that is nonzero string tension.

Perturbation theory

2021 ◽  
pp. 147-170
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Momentum Space ◽  
Feynman Diagrams ◽  
Green Functions ◽  
General Description ◽  
Loop Expansion

This chapter provides a general description of perturbation theory in terms of Feynman diagrams. The general prescriptions of constructing Feynman diagrams in momentum space are given, including for an S-matrix. The connected Green functions and the corresponding generation functional are defined with full proofs. After introducing effective action, the chapter addresses loop expansion. The chapter ends with a discussion of Feynman diagrams in fermionic theory.

scholarly journals On the loop expansion of the effective action

2007 ◽  
Vol 14 (2) ◽  
pp. 65-73
Author(s):  
Tran Huu Phat ◽  
Nguyen Van Long
Keyword(s):  
Effective Action ◽  
Finite Density ◽  
Loop Expansion ◽  
Starting Point

Based on the DeWitt formula the loop expansion of the effective action is easily established. Extending to the system with finite density we develop the in-medium DeWitt formula, which is the starting point for setting up loop expansion of the in-medium effective action.

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