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Quantum Field Theory

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Author(s): B. Allanach, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; quantum mechanics; quantum physics; quantum field theory; modern physics

Introduction
Classical field theory
Classical fields
Lorentz invariance
Symmetries and Noether's theorem for field theories
Hamiltonian mechanics
Free field theory
Review of simple harmonic oscillator
The quantum field
Real scalar fields
Complex scalar fields
The Heisenberg picture
Propagators
Interacting fields
Interaction Lagrangians
Interaction picture
Wick's theorem
Feynman diagrams
Amplitudes
Correlation functions and vacuum bubbles
Spinors
The Lorentz group and the Lorentz algebra
The Clifford algebra and the spin representation
Properties of the spin representation
The Dirac equation
Chiral/Weyl spinors and gamma5
Parity operator
Solutions to Dirac's equation
Symmetries and currents
Quantizing the Dirac field
Fermion quantization
Yukawa theory
Feynman rules
Quantum electrodynamics
Classical electrodynamics
Quantization of the electromagnetic field
Coupling to matter in classical field theory
Quantization of interactions
Computations and diagrams
Index