The Path Integral in Quantum Mechanics and in the Quantum Field Theory
Lecturer
Date
22nd October ~ 12th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday,Friday | 15:20 - 16:55 | Shuangqing-B534 | Zoom 17 | 442 374 5045 | BIMSA |
Syllabus
1.The Path Integral in Quantum Mechanics.
Introduction. The Classical Action. The Quantum Mechanical Amplitude. The Classical Limit. The Sum Over Paths. The Path Integral. The Rule for Two Events. Extension to Several Events. The Free Particles. The Wave function. Gaussian Integrals. Motion in a Potential Field. The Path Integral as a Functional. Interaction of a Particle and Harmonic Oscillator. Evaluation of Path Integrals by Fourier Series. The Schrodinger Equation.
2.Path Integral In Quantum Field Theory.
Introduction. The Path Integral. Generating functionals. Where is the i-epsilon?? Gauge Invariance. Fermionic Path Integral. Schwinger-Dyson Equations. Ward Takahashi Identity.
3.Renormalization.
Casimir Effect. Hard Cutoff. Regular Independence. Scalar Field Theory Example. Vacuum Polarization . Scalar Theory. Vacuum Polarization in QED. Physics of Vacuum Polarization. The anomalous Magnetic Moment. Extracting the Moment. Evaluating the Graphs. Mass Renormalization. Vacuum Expectation Values. Electron Self-Energy. Pole Mass. Minimal Subtraction. Summary and Discussion. Renormalized Perturbation Theory. Counterterms.Two-point Functions. Three-point functions. Renormalization Conditions in QED. $Z_1 =Z_2$: implications and proof. Infrared Divergences. $e^+e^- \to \mu^+\mu^- (+\gamma)$. Jets. Other Loops. A Dimensional Regularization. Renormalizability. Renormalizabilty of GED . Non-Renormalizable Field Theories. Non-Renormalizable Theories. The Schrodinger Equation. The 4-Fermi Theory. Theory of Mesons. Quantum Gravity . Summary of Non-Renormalizable Theories. Mass Terms and Naturalness. Super-Renormalizable Theories.
Introduction. The Classical Action. The Quantum Mechanical Amplitude. The Classical Limit. The Sum Over Paths. The Path Integral. The Rule for Two Events. Extension to Several Events. The Free Particles. The Wave function. Gaussian Integrals. Motion in a Potential Field. The Path Integral as a Functional. Interaction of a Particle and Harmonic Oscillator. Evaluation of Path Integrals by Fourier Series. The Schrodinger Equation.
2.Path Integral In Quantum Field Theory.
Introduction. The Path Integral. Generating functionals. Where is the i-epsilon?? Gauge Invariance. Fermionic Path Integral. Schwinger-Dyson Equations. Ward Takahashi Identity.
3.Renormalization.
Casimir Effect. Hard Cutoff. Regular Independence. Scalar Field Theory Example. Vacuum Polarization . Scalar Theory. Vacuum Polarization in QED. Physics of Vacuum Polarization. The anomalous Magnetic Moment. Extracting the Moment. Evaluating the Graphs. Mass Renormalization. Vacuum Expectation Values. Electron Self-Energy. Pole Mass. Minimal Subtraction. Summary and Discussion. Renormalized Perturbation Theory. Counterterms.Two-point Functions. Three-point functions. Renormalization Conditions in QED. $Z_1 =Z_2$: implications and proof. Infrared Divergences. $e^+e^- \to \mu^+\mu^- (+\gamma)$. Jets. Other Loops. A Dimensional Regularization. Renormalizability. Renormalizabilty of GED . Non-Renormalizable Field Theories. Non-Renormalizable Theories. The Schrodinger Equation. The 4-Fermi Theory. Theory of Mesons. Quantum Gravity . Summary of Non-Renormalizable Theories. Mass Terms and Naturalness. Super-Renormalizable Theories.
Video Public
Yes
Notes Public
Yes
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.