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8.323

Relativistic Quantum Field Theory I

4-0-8 units · Graduate

A one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics. Topics: classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields, spin fields, and Gauge bosons. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.

Spring 2023

Topics

  • Classical Field Theories and Principle of Locality
  • Symmetries and Conservation Laws
  • Why Quantum Field Theory
  • Canonical Quantization of a Free Scalar Field Theory
  • Complex Scalar Field Theory and Antiparticles
  • Propagators and Green Functions
  • Interacting Theories and S-matrix
  • Path Integral Formalism for Non-Relativistic Quantum Mechanics
  • Path Integral Formalism for QFT, and Computation of Time-Ordered Correlation Functions
  • Time-Ordered Correlation Functions in Field Theory
  • Computation of Correlation Functions in Perturbation Theory and Feynman Diagrams
  • More on Perturbation Theory and Feynman Diagrams
  • Introducing the Dirac Equation
  • Lorentz Covariance of the Dirac Equation
  • Classical Solutions of Dirac Equations
  • Quantization of the Dirac Theory
  • Chiral and Majorana Spinors
  • Discrete Symmetries
  • Path Integrals of Fermions
  • Maxwell Theory and its Canonical Quantization
  • Quantum Maxwell Theory (continued)
  • Quantum Electrodynamics
  • Cross Section and Decay Rate
  • Elementary Processes in QED (I)
  • Elementary Processes in QED (II)
  • Quantum Fluctuations and Renormalization

Readings

  • Peskin, Michael E., and Daniel V. Schroeder. An Introduction to Quantum Field Theory . CRC Press, 1995. ISBN: 9780201503975. (A comprehensive and pedagogical treatment of QFT starting from the basics and reaching up to the physics of the standard model.)
    Required
  • Weinberg, Steven. The Quantum Theory of Fields, Volume 1: Foundations. Cambridge University Press, 2005. ISBN: 9780521670531. (A comprehensive and insightful treatment of the foundations of QFT.)
    Required
  • [P&S] = Peskin, Michael E., and Daniel V. Schroeder. An Introduction to Quantum Field Theory . CRC Press, 1995. ISBN: 9780201503975. (A comprehensive and pedagogical treatment of QFT starting from the basics and reaching up to the physics of the standard model.)
    Required
  • [SW] = Weinberg, Steven. The Quantum Theory of Fields, Volume 1: Foundations. Cambridge University Press, 2005. ISBN: 9780521670531. (A comprehensive and insightful treatment of the foundations of QFT.)
    Required
  • Zee, Anthony. Quantum Field Theory in a Nutshell . Princeton University Press, 2003. ISBN: 9780691010199. (A fun book that deals briefly with many of the key ideas and uses of QFT.)
    Recommended
  • Srednicki, Mark. Quantum Field Theory . Cambridge University Press, 2007. ISBN: 9780521864497. (Very readable and comprehensive. Structured somewhat differently from this course. Part I (spin 0) and Part II (spin 1/2) are available at Quantum Field Theory: Spin Zero and Quantum Field Theory: Spin One Half .) ↗
    Recommended
  • Banks, Tom. Modern Quantum Field Theory: A Concise Introduction . Cambridge University Press, 2008. ISBN: 9780521850827. (Modern, insightful treatment of many important topics.)
    Recommended
  • Schwartz, Matthew. Quantum Field Theory and the Standard Model . Cambridge University Press, 2013. ISBN: 9781107034730. (A well-written introduction to QFT that emphasizes physical intuition alongside calculations. Self-contained, and covers both canonical quantization and the path integral approach.)
    Recommended
  • Brown, Lowell S. Quantum Field Theory . Cambridge, UK: Cambridge University Press, 1994. ISBN: 9780521469463. (A modern path integral presentation of QFT. Covers QED but not QCD.)
    Recommended
  • Ramond, Pierre. Field Theory: A Modern Primer (second edition). Levant Books, 2007. ISBN: 9788187169840. (A book dealing efficiently with QFT in the path integral approach.)
    Recommended
  • Ryder, Lewis. Quantum Field Theory (second edition). Cambridge University Press, 1996. ISBN: 9780521478144. (A modern pedagogical introduction to QFT including the Weinberg-Salam model and other selected topics.)
    Recommended
  • Mandl, Franz, and Graham Shaw. Quantum Field Theory. John Wiley & Sons, 1984. ISBN: 9780471906506. (A clear and concise introduction to the basic computations in quantum field theory.)
    Recommended
  • Problem Sets: Problem Set 1 · Readings: [P&S] Sections 2.1–2.2 [SW] Chapter 1
    Reading assignment
  • Problem Sets: Problem Set 2 · Readings: [P&S] Chapter 2 [SW] Chapter 1
    Reading assignment
  • Problem Sets: Problem Set 3 · Readings: [P&S] Chapter 2 [SW] Chapter 1
    Reading assignment
  • Problem Sets: Problem Set 4 · Readings: [P&S] Sections 4.1–4.4 and 9.1–9.2
    Reading assignment
  • Problem Sets: Problem Set 5 · Readings: [P&S] Sections 4.1–4.4 and 9.1–9.2
    Reading assignment
  • Problem Sets: Problem Set 6 · Readings: [P&S] Sections 4.1–4.6 and 9.1–9.2
    Reading assignment
  • Problem Sets: Problem Set 7 · Readings: [P&S] Chapter 3
    Reading assignment
  • Problem Sets: Problem Set 8 · Readings: [P&S] Chapter 3
    Reading assignment
  • Problem Sets: Problem Set 9 · Readings: [P&S] Chapter 3
    Reading assignment
  • Problem Sets: Problem Set 10 · Readings: [P&S] Chapter 3, Section 4.7, and Section 9.5
    Reading assignment
  • Problem Sets: Problem Set 11 · Readings: [P&S] Section 9.4
    Reading assignment
  • Problem Sets: Problem Set 12 · Readings: [P&S] Sections 4.5–4.8 and Chapter 5
    Reading assignment

Prerequisites & course information

Prereq: 8.321 G (Spring) 4-0-8 units

Sources