PHY3068 - Module Description

MODULE TITLE	Principles of Theoretical Physics					CREDIT VALUE	15
MODULE CODE	PHY3068		MODULE CONVENER			Dr A.V. Shytov

DURATION	TERM	1	2	3	Number Students Taking Module (anticipated)		19
	WEEKS		T2:01-11

DESCRIPTION – summary of the module content (100 words)

This module reviews the most important concepts of theoretical physics, in particular: the action, symmetries, and conservation laws. It shows how they help physicists to think about seemingly disconnected topics, ranging from mechanics to quantum field theory. The module is recommended as an option for students who wish to specialise in theoretical physics, and who are intending to take level 7 theory option(s), such as PHYM013 Quantum Many-Body Theory. The topics covered will be also of interest to the students who want to understand the language of theoretical physics without making it their field of research.

MODULE AIMS – intentions of the module

Theoretical physics aims to organise our knowledge about the physical world using a compact set of principles that are expressed mathematically.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

use symmetry principles to determine the form of the action of a physical system;
derive equations of motion and conservation laws using the action;
apply the concept of energy-stress tensor to a range of problems;
describe the relation between least-action principle in classical theory and path integral approach in quantum theory;
solve quantum-mechanical problems involving magnetic field;
use the semiclassical approximation in quantum mechanics to solve problems;

Discipline Specific Skills and Knowledge:

apply the ideas and approaches of theoretical physics to a wide range of problems;

Personal and Key Transferable / Employment Skills and Knowledge:

devise a well-structured solution with clearly explained reasoning;
use a range of resources in order to learn through independent study.

SYLLABUS PLAN – summary of the structure and academic content of the module

Analytical dynamics
least action principle, Euler-Lagrange equations, symmetries, Noether's theorem, conservation laws.
Relativistic mechanics
geometry of space time, Lorentz symmetry, action, equations of motion, particle in external fields, scalar and vector potentials.
Classical field theory
scalar field, its action and conservation laws, sound waves in gases and solids as an example.
Electromagnetic Fields
Electromagnetic field tensor, action for electromagnetic field, Maxwell's equations, gauge invariance and charge conservation. Electromechanical analogy and the effective action.
Quantum theory
Schrödinger equation and its Green function, Heisenberg representation, path integral formulation of quantum mechanics, path integral treatment of quantum harmonic oscillator
Semiclassical Methods
Semiclassical approximation in quantum mechanics, the saddle point method.
Electromagnetic fields in quantum theory
Gauge invariance, Aharonov-Bohm effect, Landau levels
Introduction to Quantum Field Theory
Interactions mediated by virtual particles

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching activities

22 hours

Guided independent study

128 hours

Placement/study abroad

0 hours

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS