M.Sc. (Physics) curriculum, Tribhuvan University 2073

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PHY601: Quantum Field Theory 3 CH (45L+15T) Nature of the course: Theory Full Marks: 75 Pass Marks: 37.5 Course Description:

This course is aimed to provide knowledge regarding relativistic particles and the importance of field concepts for those systems.

Objectives:

The objective of this course is to train the students in the methods of relativistic Quantum Mechanics. At the completion of the course, the student should be able to solve problems in Quantum Mechanics

Course Contents:

1. Relativistic Single Particle Theory (Zero Spin): [5 hours] 1.1. Klein-Gordon equation, 1.2. Physical Interpretation, 1.3. Charged Spin-zero Free Particle, 1.4. Eigenvalues of Operators, 1.5. Interaction with Electromagnetic Field.

2. Relativistic single particle theory (Half Spin): [12 hours]

2.1 Dirac Equation: Dirac Matrices, 2.2 Charge density and charge current density, basic matrices, 2.3 Spin of a Dirac Particle, 2.4 Free Particle Solutions: Dirac Positron, 2.5 Solution for Neutrino, 2.6 Velocity of Dirac Particle: Zitterbewegung, 2.7 Magnetic Moment, 2.8 Charge Conjugation, 2.9 Exact Solution of Central potential problems: Hydrogen Atom, 2.10 Dirac Particle in One-dimensional Box

3. Method of Second Quantization: [6 hours]

3.1 Bosons, 3.2 Fermions, 3.3 System of Interacting Nosons: Superfludity, 3.4 System of Interacting Fermions: Superconductivity.

4. Klein-Gordon Field: [5 hours] 3.1 Klein-Gordon Field as Harmonic Oscillator, 3.2 Klein-Gordon Field in Space-Time: Casualty, 3.3 Klein-Gordon Propagator.

5. Dirac Field: [12 hours]

4.1 Lorentz Invariance in Dirac Field, 4.2 Weyl Spinors,

M.Sc. (Physics) curriculum, Tribhuvan University 2073

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4.3 Dirac Matrices: spin and gamma, 4.4 Dirac Field Bilinears, 4.5 Quantization of the Dirac Field, 4.6 Dirac Propagator, 4.7 Discrete Symmetries in the Dirac Theory.

6. Interacting Field: [5 hours]

5.1 Perturbation Theory, 5.2 Perturbation Expansion of Correlation Function, 5.3 Wick’s Theorem.

Text Books:

1. Peskin M. E and Schroeder D. V. – An Introduction to Quantum Field Theory, Perseus

Books Publishing (1995).

2. Agrawal B. K. and Hari Prakash - Quantum Mechanics, Prentice Hall of India (1977).

Reference Books:

1. Weinberg, Steven – The Quantum Theory of Fields, Vol. I. Cambridge University Press,

(2005).

2. Greiner, Walter – Field Quantization, Springer (2006).

3. Zee, Tony – Quantum Field Theory in a Nutshell, Princeton University Press (2003).

4. Nair, V. P. – Quantum Field Theory: A Modern Perspective, Springer (2005).

5. Griffiths, David – Introduction to Elementary Particles, Wiley (1987).

6. Wachter A. – Relativistic Quantum Mechanics, Springer (2011).