## Details of PH4106 (Autumn 2016)

 Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH4106 Basics of Field Theory and Relativistic Quantum Mechanics Prasanta K. Panigrahi

Preamble
This is an introductory course on 'Field Theory' for undergraduate (BS-MS and PBIP) students. Basic concepts and language of 'field theory' is introduced as a technique which has applications in 'Particle physics' as well as in ''Condensed matter physics' and 'Statistical mechanics'.

Concepts of 'field' and 'vacuum state' are discussed as an extension of (quantum) mechanics of point particles in the long wave length approximation. Relativistic quantum theory of 'spin-0 Bosons' , 'spin-1/2 Fermions' and quantization of electromagnetic fields are main contents of this course . Finally some physical applications of 'quantum field theory' are illustrated with examples.

Syllabus

• General introduction: Point particles to Fields, Long wave length approximation of harmonic lattice and phonons.

• Scalar Field Theory: Extension of quantum mechanics to relativistic particles, Klein-Gordon equation, Conservation laws, negative energy states, quantization of the scalar field and the Fock space, the Feynman propagator.

• Canonical Formalism: Lagrangian density, Symmetries, Noethers's theorem, Lorentz invariance, Gauge invariance.

• Dirac Field: Dirac Equation and Dirac algebra, Lorentz Transformations, Hole and Dirac sea, Time reversal and charge conjugation, Massless particles, Nonrelativistic limit and spin-orbit coupling, quantization of the Dirac field and the Pauli exclusion principle,the propagator.

• S-Matrix Theory: Interaction picture and adiabatic switching, S-matrix and scattering, Two point correlation function scalar and Dirac field this may be introduced in the context of free field theory as suggested above), time-ordered and normal products, the Dyson expansion and Wick's Theorem, Feynman rules for self interacting scalar theory.

• Electromagnetic field: Canonical formalism, quantization and gauge fixing, the propagator, the local gauge invariance and the covariant derivative, coupling to scalar and Dirac fields. Quantum electrodynamics, Feynman rules and simple applications.

• Applications: Klein paradox, vacuum fluctuation and Casimir effect, Lamb shift, anomalous magnetic moment, broken symmetry

Prerequisite
Intermediate Quantum Mechanics,Intermediate Classical mechanics,Intermediate Electricity and Magnetism,Advanced Quantum Mechanics, Mathematical Methods of Physics

References

1. Quantum Field Theory, From Operators to Path Integrals, Kerson Huang, Publisher:Wiley

2. The Quantum Theory of Fields, Vol. 1, Steven Weinberg. Publisher: Cambridge University Press

3. Quantum Field Theory, Claude Itzykson and Jean Bernard Zuber, Publisher: McGraw-Hill.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Elective
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Elective
6 MS 7 Elective
7 RS 1 Elective
8 RS 2 Elective