The Physical Renormalization of Quantum Field Theories

Binger, Michael William. ; /Stanford U., Phys. Dept. /SLAC

Stanford Linear Accelerator Center

关键词: Supersymmetry Theory-Hep,Hepph, Hepth;    Field Theories;    Theory-Hep,Hepph, Hepth;    71 Classical And Quantum Mechanics, General Physics;    Perturbation Theory;   

DOI  :  10.2172/899841
RP-ID  :  SLAC-R-854
RP-ID  :  AC02-76SF00515
RP-ID  :  899841

美国|英语

来源: UNT Digital Library

【 摘 要 】

The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.