Two-loop renormalization group equations in a general quantum field theory (II). Yukawa couplings

1984 ◽  
Vol 236 (1) ◽  
pp. 221-232 ◽  
Author(s):  
Marie E. Machacek ◽  
Michael T. Vaughn
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Quantum Field ◽  
Yukawa Couplings ◽  
General Quantum ◽  
Renormalization Group Equations

scholarly journals DIRAC RELATION AND RENORMALIZATION GROUP EQUATIONS FOR ELECTRIC AND MAGNETIC FINE STRUCTURE CONSTANTS

1999 ◽  
Vol 14 (40) ◽  
pp. 2797-2811 ◽  
Author(s):  
L. V. LAPERASHVILI ◽  
H. B. NIELSEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Fine Structure ◽  
Small Region ◽  
Quantum Field ◽  
Dual Symmetry ◽  
Renormalization Group Equations ◽  
Structure Constants

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants — electric α and magnetic [Formula: see text] — were obtained. It was shown that the Dirac relation is valid for the renormalized α and [Formula: see text] at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: 0.25≲α, [Formula: see text] with [Formula: see text] given by the Dirac relation: [Formula: see text].

scholarly journals SCHEME INDEPENDENCE AS AN INHERENT REDUNDANCY IN QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2071-2074 ◽  
Author(s):  
JOSÉ I. LATORRE ◽  
TIM R. MORRIS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Renormalization Group Equations ◽  
Field Transformation ◽  
Exact Renormalization Group ◽  
Infinite Set

The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relation. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme independence is turned into a vector field transformation of the kernel of the exact renormalization group equation under field redefinitions.

Renormalization

2021 ◽  
pp. 171-222
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Dimensional Regularization ◽  
General Concept ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Subtraction Procedure ◽  
Renormalization Group Equations

This chapter describes in detail the general concept of renormalization. It starts with a discussion of the regularization of Feynman diagrams. After that, the subtraction procedure is explained in detail, followed by an introduction to the notion of a superficial degree of divergence of the diagram. On this basis, the models of quantum field theory are classified as renormalizable or non-renormalizable theories. The main arbitrariness of the subtraction procedure is fixed by imposing renormalization conditions. Special sections of this chapter are devoted to renormalization in dimensional regularization and renormalization group equations.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

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