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: assigned 3 August 2019 and due 9 August 2019 (pdf)
• Assignment 2: assigned 30 August 2019 and due 7 September 2019 (pdf)
• Midterm: 1 October 2019 (pdf)
• Midterm by CLS: 1 October 2019 (pdf)
• Main exam: 6 February 2020 (pdf) (scanned copy by Sunil Mahawar)
• Performance report has submitted to HOD on 17 October 2019.

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 0.1, 0.2: 3 August 2019
• Lecture 1, 2: Formulation of relativistic quantum theory and KG equation: 9, 10 August 2019
• Lecture 3, 4: Co-variance and applications of K.G. equation and Dirac equation: 16, 17 August 2019
• Holiday: Krishna Janmashtami: 23 August 2019
• No class: Meeting at Maharani College: 24 August 2019
• Lecture 5, 6: Continuity equation for Dirac field and electron at rest: 30 August 2019
• Lecture 7: Electron in EM field and co-variance of Dirac equation: 31 August 2019
• Lecture 8, 9: Covariant form of Dirac equation: 6, 7 September 2019
• Lecture 10, 11, 12: Invariance of Dirac equation and proper transformation: 13, 14 September 2019
• Lecture 13, 14, 15: Algebra of gamma matrices: 20, 25, 27 September 2019
• Lecture 16: Plane wave solution of Dirac equation in random direction: 28 September 2019
• No class from 1 October to 13 September 2019: midterm exams
• Midterm discussion class on 17 October 2019.
• No class on 18 October 2019 due to fresher's party of students.
• Lecture 17: Normalization of general free solution spinor: 19 October 2019
• No class from 20 October to 29 September 2019: Deepawali vacation
• Lecture 18, 19: Normalization and closer relation of Dirac spinors: 1, 2 November 2019
• Lecture 20: Polarization of electron: 8 November 2019
• No class on 9 November 2019 declared by state government.
• Lecture 21: : 15 November 2019
• Lecture 22: : 16 November 2019
• No class on 22 November 2019: Lecture was not prepared.
• Lecture 23: 23 November 2019
• Lecture 24: 29 November 2019
• Lecture 25: 30 November 2019