About the course

This is a Masters in Physics course at Department of Physics, University of Rajasthan, Jaipur.

Several textbooks will be used during the course. For the following part, book by Bjorken and Drell is recommended.

Details about these books can be found by clicking here: (Merzbacher, Bjorken-Drell, Greiner and J.J. Sakurai).

Reference in book: BD-page18, page37,

The course contents are as follows:

1. Relativistic Formulation and Dirac Equation: Attempt for relativistic formulation of quantum theory, The Klein-Gordon equation, Probability density and probability current density, solution free particle K.G. equation in momentum representation, interpretation of negative probability density and negative energy solutions. Dirac equation for a free particle, properties of Dirac matrices and algebra of gamma matrices, non-relativisitic correspondence of the Pauli equation (inclusive of electromagnetic interaction). Solution of the free particle Dirac equation, orthogonality and completeness relations for Dirac spinors, interpretation of negative energy solution and hole theory.
2. Symmetries of Dirac Equation: Lorentz covariance of Dirac equation, proof of covariance and derivation of Lorentz boost and rotation matrices for Dirac spinors, Projection operators involving four momentum and spin, Parity (P), charge conjugation (C), time reversal (T) and CPT operators for Dirac spinors, Bilinear covariants and their transformations, behavior under Lorentz transformation, P, C, T and CPT, expectation values of coordinate and velocity involving only positive energy solutions and the associated problems, inclusion of negative energy solution. Zitterbewegung, Klein paradox.

Assignments

• Assignment 1: (First 2 questions) due 11 August 2018; (3rd question) due 22 August 2018
• Assignment 2: (All 3 phases has gone).
• Midterm: 22 October 2018 (pdf)
• Main Exam: 26 December 2018 (pdf) (scanned original by RPS)
• Performance report is submitted to HOD and sent to Examination Controller.

Notes

There are few handwritten notes/slides that I prepare to help me to teach the course. Since, few of them are same from previous years. Although I usually use them while teaching, there are occasions when I teach something that was not written in the notes, or do not teach something that I had written in the notes. So they are not an accurate record of the course (nor are they intended to be). Also, though each set of notes is roughly matched to a given lecture, it often happens that part of the material written for a given lecture is taught in the following lecture (if I run out of time). Some of the class room questions can get their answer at this page.

• Revision lecture: 27 and 28 July 2018
• Lecture 1: Formulation of Relativistic Quantum Theory: 3 August 2018
• Lecture 2: K.G. equation and Dirac equation: 4 August 2018
• Lecture 3: Factors in Dirac matrix and their interpretation: 10 August 2018
• Lecture 4: Non-relativistic Correspondence of Dirac equation: 11 August 2018
• Holiday: In honor of former prime minister ABV: 17 August 2018
• Lecture 5: Covariant Form of Dirac equation: 18 August 2018
• Lecture 6: Introduction to gamma matrices: 24 August 2018
• Lecture 7: Some operations of gamma matrices: 25 August 2018
• Teaching off: Students election: 31 August 2018
• Lecture 8: Proof of Covariance of Dirac equation: 1 September 2018
• On leave: No class from 07 September 2018 to 22 September 2018
• Lecture 9:: 28 September 2018
• Lecture 10:: 29 September 2018
• Lecture 11:: 5 October 2018
• Lecture 12:: 6 October 2018
• Lecture 13:: 12 October 2018
• Lecture 14:: 13 October 2018
• Holiday: Dussehra Holiday: 19 October 2018
• On leave: 20 October 2018
• No class due to mid-term exam of students: 25 and 27 October 2018
• Holiday: Deepawali Holiday: 2, 3 and 9 November 2018
• Lecture 15:: 10 November 2018