An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory

Abstract

We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in terms of their series expansion coefficients and their resultant effect on the interaction coupling, in particular at a zero of the beta function away from the origin in coupling-constant space.

arXiv comment12 pages, latex

References in corpus (38)

• The four-loop beta-function in Quantum Chromodynamics
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• The three-loop QCD $\beta$-function and anomalous dimensions
• The QCD Running Coupling
• Phases of N=1 supersymmetric gauge theories in four dimensions
• Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry
• Scheme dependence and the NSVZ $\beta$-function
• The Renormalization Scale-Setting Problem in QCD
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• Non-Perturbative Dynamics in Supersymmetric Gauge Theories
• The connection between the DRED and NSVZ renormalisation schemes
• The conformal window in QCD and supersymmetric QCD
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• Relations between Observables and the Infrared Fixed-Point in QCD
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• On the particle spectrum and the conformal window
• Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ Fixed
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Consistent Perturbative Fixed Point Calculations in QCD and SQCD
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Infrared Fixed Points in the minimal MOM Scheme
• Renormalization group functions of QCD in the minimal MOM scheme
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Pade-Summation Approach to QCD Beta-Function Infrared Properties
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\overline{MS}$-based scheme
• Study of the Renormalization-Group Evolution of $\mathcal{N}=1$ Supersymmetric Gauge Theories Using Padé Approximants

Cited by in corpus (13)

• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
• Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory