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Physics
615. Overview of QFT
(Fall 2010)
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Room: ARC-212
Monday, Thursday;
12:00-1:20 PM
Instructor: Sergei
Lukyanov
office: Serin E364
office phone: (732)-445-5500 ext.4622
e-mail:
sergei@physics.rutgers.edu (the best way)
Office hours: Wednesday
2:00-4:00 pm
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Text Book: M.E. Peskin, D.V. Schroeder:
Quantum Field Theory
Westview Press, 1995
Homework: There will
be homework assignments.
Late homework
will not be accepted.
Homework will be graded and give
an important
contribution
to your final
grade
(final score =
50% Homework +
+ 50% Final).
Exams: There will be
a
final take-home exam.
Students with Disabilities:
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If you have a disability, it is essential that you speak to the course supervisor early in the semester to make the necessary arrangements to support a successful learning experience. Also, you must arrange for the course supervisor to receive a Letter of Accommodation from the Office of Disability Services.
http://www.physics.rutgers.edu/ugrad/disabilities.html |
Download this
info in PDF format
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This is a tentative schedule of what we will
cover in the course. It is subject to change,
often without notice. These will occur in
response to the speed with which we cover
material, individual class interests, and
possible changes in the topics covered. Use
this plan to read ahead from the text books,
so you are better equipped to ask questions in class.
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INTRODUCTION
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- CLASSICAL FIELD THEORY:
Lagrangian density. Example: Continuum limit of a one dimensional lattice.
Lorentz invariance. Locality and causality. Equations of motion.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 2.1, 2.2)
2) H. Goldstain: Classical Mechanics,
Addison-Wesley, 3d edition (Chapters 13.1, 13.2)
3) L.D. Landau and E.M. Lifshitz: The Classical Theory of Fields,
Buterworth Heiemann, 4th ed (Chapters 1-7)
- NOETHER's THEOREM:
Symmetry. Noether's theorem. Energy-momentum tensor. Examples.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapter 2.2)
2) H. Goldstain: Classical Mechanics,
Addison-Wesley, 3d edition (Chapters 13.3, 13.5, 13.7)
3) L.D. Landau and E.M. Lifshitz: The Classical Theory of Fields,
Buterworth Heiemann, 4th ed (Chapters 26-33)
- KLEIN-GORDON FIELD:
Hamiltonian formalism. Quantization. Fock space. Spectrum.
Causality and local commutativity in QFT. Feynman propagator.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 2.3, 2.4)
2) H. Goldstain: Classical Mechanics,
Addison-Wesley, 3d edition (Chapter 13.4, 13.6)
THE DIRAC FIELD
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- REPRESENTATIONS OF THE LORENTZ GROUP:
Representations of the infinitesimal Lorentz group.
Left- and right- handed spinors. Vector representations. Space Inversions and Time-Reversal.
The Dirac spinor. Dirac spinor bilinears. Algebra of the Dirac matrixes.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 3.1, 3.2, 3.4)
2) P. Ramond: Field Theory.
Published by Westview Press, 1997 (2d edition)
ISBN 0201304503, 9780201304503
(Chapters 1.2, 1.4)
3) L.D. Landau, E.M. Lifshitz, V.B. Berestetskii
and L.P. Pitaevskii: Quantum Electrodynamics (Course of Theoretical Physics, Volume 4)
Buterworth Heiemann, 2nd ed (Chapters 3.17-3.19, 3.22)
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THE DIRAC EQUATION:
The Dirac and Weyl Lagrangians.
Free-particle solutions of the Weyl equation.
Helicity. Free-particle solutions of the Dirac equation. Spin sums.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 3.1-3.3)
2) L.D. Landau, E.M. Lifshitz, V.B. Berestetskii
and L.P. Pitaevskii: Quantum Electrodynamics (Course of Theoretical Physics, Volume 4)
Buterworth Heiemann, 2nd ed (Chapters 3.20, 3.21, 3.23, 3.30)
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THE QUANTIZED DIRAC FIELD:
The canonical quantization of the Dirac field. The relation between the
spin and the statistics. The Dirac propagator. Grassmann numbers.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapter 3.5)
2) L.D. Landau, E.M. Lifshitz, V.B. Berestetskii
and L.P. Pitaevskii: Quantum Electrodynamics (Course of Theoretical Physics, Volume 4)
Buterworth Heiemann, 2nd ed (Chapter 3.25)
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DISCRETE SYMMETRIES OF THE DIRAC THEORY:
Symmetries in the quantum system.
Parity. Time reversal. Charge conjugation. CPT-theorem.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapter 3.6)
2) L.D. Landau, E.M. Lifshitz, V.B. Berestetskii
and L.P. Pitaevskii: Quantum Electrodynamics (Course of Theoretical Physics, Volume 4)
Buterworth Heiemann, 2nd ed (Chapters 3.26-3.28)
3)
S. Weinberg, The Quantum Theory of Fields,
Cambridge University Press, Vol.1 (Chapters 2.1-2.3 )
4) (Advanced Book Classics)
R.F. Streater and A.S. Wightman; PCT, spin and statistic and
all that. Princeton University Press, 2000
ISBN 0691070628, 9780691070629
PERTURBATION THEORY
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- INTERACTING FIELDS:
Perturbative QFT.
Relevant, marginal and irrelevant perturbations.
Examples: ``phi-fourth'' theory, Yukawa theory,
QED.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapter 4.1)
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FORMAL PERTURBATIVE EXPANSION OF CORRELATION FUNCTIONS:
Interaction picture.
Dyson series. Wick's theorem. Feynman diagrams for ``phi-fourth'' theory.
Symmetry factors. Disconected (vacuum) diagrams.
Diagramology: Fully connected and ``amputated''
correlation functions, proper verteces.
Momentum-space Feynman rules.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 4.2-4.4)
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ULTRAVIOLET DIVERGENCIES IN ``PHI-FOURTH'' THEORY:
Mass operator at the lowest perturbative order. Wick rotation.
Mass renormalization.
Counting of ultraviolet divergences. Renormolized coupling constant.
Field-strength renormalization.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 10.1, 10.2)
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RENORMALIZED PERTURBATION THEORY:
Renormalization programm. Interacting fields in $d$-dimensions.
Dimensional regularization. Renormalization schemes. Renormalization at
the leading order in ``phi-fourth'' theory.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 10.1, 10.2, 7.5 (pp.249-251))
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RENORMALIZATION GROUP EQUATION:
The massless ``phi-fourth'' theory.
Renormalization scheme.
``Critical'' submanifold.
Callan-Symanzik equation.
Renormalization group flow.
Running coupling constant.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 12.2, 12.3)
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THEORIES WITH FERMIONS:
Wick theorem. Feynman rules for fermions.
Overwiew of
renormolized perturbation theory for the pseudoscalar Yukawa theory.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 4.7, 7.5 (pp.249-251))
SCATTERING THEORY
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- ASYMPTOTIC THEORY:
Spectral assumptions. Kallen-Lehmann spectral
representation. In- and out- states.
S-matrix. The LSZ reduction formula.
Computing S-matrix elements from Feynman diagrams. Rates and cross sections.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 7.1, 7.2, 4.5, 4.6);
2)
S. Weinberg, The Quantum Theory of Fields,
Cambridge University Press, Vol.1 (Chapters 3.1, 3.2, 3.4, 3.5)
3)
C. Itzykson, J.-B. Zuber,
Quantum Field Theory, McGraw-Hill International Editions [IZ], Vol.1
(Chapter 5);
4)
R.F. Streater and A.S. Wightman; PCT, spin and statistic and
all that. Princeton University Press, 2000
ISBN 0691070628, 9780691070629;
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EXAMPLES OF S-MATRIX:
Simplest scattering amplitudes for ``phi-fourth'' and Yukawa theories.
Mandelstam variables.
Nonreletevistic limit.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 4.5-4.7)
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ELEMENTARY PROCESSES OF QED:
Feynman Rules for QED. The Coulomb Potential. e + e^+ -> mu + mu^+
and e+mu->e+mu cross secrtions.
Compton scattering.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 1, 4.8, 5.1-5.3, 5.5);
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GENERAL PROPERTIES OF S-MATRIX:
Crossing symmetry. C, P, T -invariance. Optical theorem.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 5.4, 7.3);
2)
S. Weinberg, The Quantum Theory of Fields,
Cambridge University Press, Vol.1 (Chapters 3.3, 3.6)
QED
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- UV DIVERGENCIES:
Current correlation functions. Counting of the UV divergencies.
Photon polarization operator. Non-renormalizability of
the conseved current.
Renormalized perturbation
theory. Normalization conditions.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 10.1, 10.3, 7.5);
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RADIATIVE CORRECTIONS:
Electron-photon vertex and
two particle form factors of the current. Schwinger's correction.
Infrared divergencies.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 6.1-6.5, 7.3);
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GAUGE INVARIANCE:
Electron self-energy.
Ward-Takahashi identities.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 7.1 (pp.217-222), 7.4;
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UV ASYMPTOTICS:
Vacuum polarization. Callan-Symanzick equation. Running
coupling constant. Landau pole.
Literature:
1)
M.E. Peskin, D.V. Schroeder: Quantum Field Theory
(Chapters 7.5, 12.2);
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Download
syllabus
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Homeworks and
Solutions
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The assignments and solutions are stored in PDF format.
The absolute
cutoff time for homework is 4pm due date. |
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Assigned
on
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Assignment
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Due
Date
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Solution
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Sep 2,
2010 |
pdf
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Sep 13,
2010 |
pdf
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| 2. |
Sep 13,
2010 |
pdf
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Sep 23,
2010 |
pdf
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| 3. |
Sep 23,
2010 |
pdf
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Oct 7,
2010 |
pdf
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| 4. |
Oct 7,
2010 |
pdf
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Oct 18,
2010 |
pdf
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| 5. |
Oct 18,
2010 |
pdf
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Nov 1,
2010 |
pdf
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| 6. |
Nov 1,
2010 |
pdf
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Nov 18,
2010 |
pdf
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| 7. |
Nov 18,
2010 |
pdf
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Dec 2,
2010 |
pdf
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| 8. |
Dec 2,
2010 |
pdf
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Dec 13,
2010 |
pdf
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Final exam:
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Due to Dec 20, 2010
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