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Introduction to Quantum Field Theory

Introduction to Quantum Field TheoryJohn CardyMichaelmas Term 2010 Version 13/9/10 AbstractThese notes are intended to supplement the lecture course Introduction to Quan-tum Field Theory and are not intended for wider distribution. Any errors or obviousomissions should be communicated to me A Brief History of Quantum Field Theory22 The Feynman path integral in particle Quantum mechanics Imaginary time path integrals and statistical mechanics ..73 Path integrals in Field Field Theory action functionals .. The generating functional .. The propagator in free Field Theory .. 144 Interacting Field Feynman diagrams .. Evaluation of Feynman diagrams .. 265 Analysis of divergences .. Mass, Field , and coupling constant renormalisation .. 321 QFT126 Renormalisation Callan-Symanzik equation .. Renormalisation group flows .. One-loop computation in 4theory .. Application to critical behaviour in statistical mechanics .

† 1900: Planck hypothesises the photon as the quantum of radiation. † 1920s/30s: development of particle quantum mechanics: the same rules when applied to the Maxwell fleld predict photons. However relativistic particle quantum mechanics has problems (negative energy states.) † 1930s/40s: realisation that relativity + quantum mechanics ...

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