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

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].

COVARIANT DERIVATIVE EXPANSION FOR NON-LINEAR σ-MODEL WITH TWO MULTIPLETS

1989 ◽  
Vol 04 (21) ◽  
pp. 2049-2054
Author(s):  
MIZUHIKO HOSOKAWA ◽  
WATARU ISHIZUKA ◽  
YUKIO KIKUCHI
Keyword(s):  
Covariant Derivative ◽  
Derivative Expansion ◽  
Non Linear

The covariant derivative expansion is generalized to the case of two multiplets in the non-linear σ-model.

scholarly journals STrEAMlining EFT Matching

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Timothy Cohen ◽  
Xiaochuan Lu ◽  
Zhengkang Zhang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Covariant Derivative ◽  
Arbitrary Order ◽  
Effective Field ◽  
Derivative Expansion ◽  
Mass Expansion

This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in Ref. [1]. The code and an example notebook are available at this link.

scholarly journals A relativistic basis of the quantum theory.—II

1934 ◽  
Vol 145 (855) ◽  
pp. 645-656 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
General Expression ◽  
Matrix Equation ◽  
Covariant Derivative ◽  
Riemannian Geometry ◽  
Order Equation ◽  
Second Order ◽  
Space Curvature

The paper is a continuation of the last paper communicated to these 'Proceedings.' In that paper, which we shall refer to as the first paper, a more general expression for space curvature was obtained than that which occurs in Riemannian geometry, by a modification of the Riemannian covariant derivative and by the use of a fifth co-ordinate. By means of a particular substitution (∆ μσ σ = 1/ψ ∂ψ/∂x μ ) it was shown that this curvature takes the form of the second order equation of quantum mechanics. It is not a matrix equation, however but one which has the character of the wave equation as it occurred in the earlier form of the quantum theory. But it contains additional terms, all of which can be readily accounted for in physics, expect on which suggested an identification with energy of the spin.

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