scholarly journals The fermionic universal one-loop effective action

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sebastian A. R. Ellis ◽  
Jérémie Quevillon ◽  
Pham Ngoc Hoa Vuong ◽  
Tevong You ◽  
Zhengkang Zhang
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Covariant Derivative ◽  
Heavy Fermion ◽  
Axial Vector ◽  
Derivative Expansion ◽  
Universal Structure ◽  
Pseudo Scalar ◽  
Matching Techniques ◽  
Analytical Expressions

Abstract Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions (Dirac or Majorana) with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops [13].

A CHIRALLY SYMMETRIC EFFECTIVE ACTION FOR VECTOR AND AXIAL VECTOR FIELDS IN A GLOBAL COLOR SYMMETRY MODEL OF QCD

1989 ◽  
Vol 04 (07) ◽  
pp. 1681-1733 ◽  
Author(s):  
C. D. ROBERTS ◽  
J. PRASCHIFKA ◽  
R. T. CAHILL
Keyword(s):  
Effective Action ◽  
Bound States ◽  
Vector Fields ◽  
Axial Vector ◽  
Form Factors ◽  
Local Fields ◽  
Local Action ◽  
Massless Fermion ◽  
Yang Mills ◽  
Local Functions

We consider the quantum field theory of a model of an extended Nambu-Jona-Lasinio type with a QCD based nonlocal fermion current-current interaction which has global SU(Nc) symmetry. We obtain an exact bosonization of this model in four Euclidean dimensions using auxiliary bilocal fields and discuss the dynamical breakdown of chiral symmetry in the massless fermion limit. A local field bosonization is obtained by decomposing the bilocal fields in terms of complete orthonormal sets of functions with the expansion coefficients, which are local functions, identified as the local meson fields. Retaining the ground state pseudoscalar, vector and pseudovector local fields we obtain a local effective action for this sector of the theory. The derivative expansion of the fermionic determinant necessary to obtain this local action is self-regularizing because of the bilocal substructure present in the model which is manifest in the form factors that are associated with the local fields. In our local action the value of each coefficient depends critically on the underlying fermionic dynamics through these form factors and the vacuum functions. As a consequence of this the vector and pseudovector fields in the theory are best interpreted as simple fermion-antifermion bound states rather than as massive Yang-Mills fields or exotic composites of the pseudoscalars; interpretations that we find are not in general admitted when models such as the GCM are treated correctly. Identifying then the physical vector and pseudovector fields with the linearly transforming chiral partners introduced by the bosonization, we obtain an effective action for this sector of the meson spectrum which predicts values for the kinematic and dynamic quantities associated with these fields.

scholarly journals Derivative expansion at small mass for the spinor effective action

2011 ◽  
Vol 83 (10) ◽  
Author(s):  
Gerald V. Dunne ◽  
Adolfo Huet ◽  
Jin Hur ◽  
Hyunsoo Min
Keyword(s):  
Effective Action ◽  
Small Mass ◽  
Derivative Expansion

scholarly journals An All-Orders Derivative Expansion

1997 ◽  
Vol 12 (06) ◽  
pp. 1143-1151 ◽  
Author(s):  
Gerald Dunne
Keyword(s):  
Magnetic Field ◽  
Effective Action ◽  
Exact Result ◽  
Inhomogeneous Magnetic Field ◽  
Derivative Expansion ◽  
Spatially Inhomogeneous ◽  
Convergent Expansion

We evaluate the exact QED2+1 effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders derivative expansion of the effective action, and indicates that the derivative expansion is an asymptotic, rather than a convergent, expansion.

scholarly journals One-loop matching and running with covariant derivative expansion

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Brian Henning ◽  
Xiaochuan Lu ◽  
Hitoshi Murayama
Keyword(s):  
Covariant Derivative ◽  
Derivative Expansion
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