The Quantum Field Theory

This is a course on Introduction to quantum field theory, normally taught as a first semester of quantum field theory for physics graduate students.

Lecturer

Hrachya Babujyan

Date

15th October ~ 10th December, 2024

Location

Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|

Tuesday,Thursday | 15:20 - 16:55 | A3-2-303 | ZOOM 07 | 559 700 6085 | BIMSA |

Prerequisite

Basic knowledge of quantum mechanics and classical electrodynamics.

Syllabus

The major themes of the course are the basic fundamental concepts and building blocks of modern quantum field theory.

1.The Introduction.

The birth of the Quantum Field Theory.

2.The microscopic theory of radiation.

Blackbody radiation. Einstein coefficients. Quantum Field Theory.

3.Lorenz Invariance and second quantization.

Lorenz invariance. Classical plane waves as oscillators. Second quantization.

4.Classical Field theory.

Hamiltonians and Lagrangians. The Euler-Lagrange Equations. Noether’s theorem. Coulomb’s law. Green’s functions.

5.Old-fashioned perturbation theory.

Lippman-Schwinger equation. Early infinities.

6.The Cross sections.

Non-relativistic limit. Electron positron Scattering.

7.The S-matrix and time-ordered products.

The LSZ reduction formula. The Feynman propagator.

8. Feynman rules.

Lagrangian derivation. Hamiltonian derivation. Momentum-Space. F1eynman rules. Examples. Normal ordering and Wick’s theorem.

1.Spin 1 and gauge invarian6ce.

Unitary representations of the Poincare group. Embedding particles into fields. Covariant derivatives. Quantization and the Ward identity. The photon propagator. Is gauge invariance real? Higher spin fields.

2. Scalar Quantum electrodynamics.

Quantizing complex scalar fields. Feynman rules for scalar QED. Scattering in scalar QED. Ward identity and gauge invariance. Lorenz invariance and charge conservation.

3. Spinors.

Representation of the Lorenz group. Spinor representation. Dirac matrices. Coupling to the photon. What does spin ½ mean? Majorana and Weyl fermions.

4. Spinor solutions and CPT.

Chirality, helicity and spin. Solving the Dirac equation. Majorana spinors. Charge conjugation. Parity. The time reversal.

5. Spin and Statistics.

Identical particles. Spin-statistics from path dependence. Quantizing spinors. Lorenz invariance of the S-matrix. Stability. Causality.

6. Quantum Electrodynamics.

QED Feynman rules. Gamma matrix identities. Electron positron Scattering. Rutherford scattering. Compton Scattering. Historical note.

Introduction. The Path integral. Generating functionals. Where is the I$\epsilon$. Gauge invariance. Fermionic path Integral. Schwinger Dyson Equations. Ward Takahashi identity.

**A. Field Theory**1.The Introduction.

The birth of the Quantum Field Theory.

2.The microscopic theory of radiation.

Blackbody radiation. Einstein coefficients. Quantum Field Theory.

3.Lorenz Invariance and second quantization.

Lorenz invariance. Classical plane waves as oscillators. Second quantization.

4.Classical Field theory.

Hamiltonians and Lagrangians. The Euler-Lagrange Equations. Noether’s theorem. Coulomb’s law. Green’s functions.

5.Old-fashioned perturbation theory.

Lippman-Schwinger equation. Early infinities.

6.The Cross sections.

Non-relativistic limit. Electron positron Scattering.

7.The S-matrix and time-ordered products.

The LSZ reduction formula. The Feynman propagator.

8. Feynman rules.

Lagrangian derivation. Hamiltonian derivation. Momentum-Space. F1eynman rules. Examples. Normal ordering and Wick’s theorem.

**B. Quantum Electrodynamics**1.Spin 1 and gauge invarian6ce.

Unitary representations of the Poincare group. Embedding particles into fields. Covariant derivatives. Quantization and the Ward identity. The photon propagator. Is gauge invariance real? Higher spin fields.

2. Scalar Quantum electrodynamics.

Quantizing complex scalar fields. Feynman rules for scalar QED. Scattering in scalar QED. Ward identity and gauge invariance. Lorenz invariance and charge conservation.

3. Spinors.

Representation of the Lorenz group. Spinor representation. Dirac matrices. Coupling to the photon. What does spin ½ mean? Majorana and Weyl fermions.

4. Spinor solutions and CPT.

Chirality, helicity and spin. Solving the Dirac equation. Majorana spinors. Charge conjugation. Parity. The time reversal.

5. Spin and Statistics.

Identical particles. Spin-statistics from path dependence. Quantizing spinors. Lorenz invariance of the S-matrix. Stability. Causality.

6. Quantum Electrodynamics.

QED Feynman rules. Gamma matrix identities. Electron positron Scattering. Rutherford scattering. Compton Scattering. Historical note.

**C. Path Integrals**Introduction. The Path integral. Generating functionals. Where is the I$\epsilon$. Gauge invariance. Fermionic path Integral. Schwinger Dyson Equations. Ward Takahashi identity.

Video Public

Yes

Notes Public

Yes

Language

English

Lecturer Intro

Hrachya Babujian (Babujyan) received his PhD from L. D. Landau Institute of Theoretical Physics in Moscow, where he was PhD student of A.A. Belavin. The Habilitation he get in Yerevan Physics Institute (Alikhanyan National Lab) where he currently holds the title Leading Scientific Researcher. In the 1990’s he was working in Bonn University and Berlin FU where he enjoy the Mathematical Physics group of R. Schrader. He also work in Sao Carlos University (Brazil) in Brookhaven National Lab, Simons Center and Chicago University. H. Babujian’s research interests are in Integrability in 2d statistical models and 1+1 dimensional quantum field theories, 1d spin chains, conformal blocks, form factors and thermodynamics of integrable models. Now his interest is the applications of the exact form factors in 1+3 dimensional lepton-hadron scattering in small Bjorkan x case.