Transcription of Physics 198-730B: Quantum Field Theory
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Physics 198-730B: Quantum Field Theory
Preprint MCGILL-98/NNhep-ph/yymmnnnPhysics 198-730B: Quantum Field TheoryJames M. Cline1 Dept. of Physics , McGill University3600 University , PQ H3A 2T8 CanadaThis course builds on the introduction to QFT you received in198-610A. We will startwith the loop expansion in scalar Field Theory to illustrate the procedure of renormalization,and then extend this to QED and other gauge theories. My goal is to introduce all of themost important concepts and developments in QFT. We cannot treat them all in depth, butyou will learn the basic ideas. The topics to be covered (timepermitting) will include: Perturbation Theory : the loop expansion; regularization;dimensional regularization;Wick rotation; momentum cutoff; 4theory; renormalization; renormalization groupequation; Wilsonian viewpoint; the epsilon expansion; relevant, irrelevant and marginaloperators; Callan-Symanzik equation; running couplings;beta function; anomalousdimensions; IR and UV fixed points; asymptotic freedom; triviality; Landau pole The effective action: generating functional; connected diagrams; one-particle-irreduciblediagrams; Legendre transform Gauge theories: QED; QCD; anomalies; gauge invariance and unitarity; gauge fixing;Faddeev-Popov procedure; ghosts; unitary gauge; covariant gauges; Ward Identities;BRS t
Figure 2.5. Complex contour for evaluating complex Gaussian integral. Now let’s return to the 4-point function. When we do the contractions, we have the possibility of contracting the external fields with the fields from the interaction vertex. This new connected contribution (figure 3) comes in addition to the disconnected one shown in ...
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