PH40073: Mathematical physics
[Page last updated: 21 April 2022]
Academic Year:  2022/3 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take PH20029 OR take PH20067 
Learning Outcomes:  After taking the section on phase transitions the student should be able to:
* perform mean field calculations of phase transitions; * define critical exponents and discuss scaling relations and universality classes; * describe in detail the principles of realspace renormalisation; After taking the section on classical mechanics the student should be able to: * show proficiency in using the Lagrangian and Hamiltonian formulations to solve problems in classical mechanics; * use symmetries to derive conservation laws; * formulate and analyse equations of motion for systems of oscillators; * analyse nonlinear field models using methods of classical mechanics. 
Aims:  The aim of this unit is to develop students' understanding of some fundamental aspects of Physics, where a mathematical treatment is essential fully to appreciate the subject. For the section on phase transitions, the aim is for students to gain a quantitative understanding of the principles that govern first and second order phase transitions. For the section on classical mechanics, the aim is for students to understand and apply the Lagrangian formulation of classical mechanics. 
Skills:  Numeracy T/F A, Problem Solving T/F A. 
Content:  Phase transitions: Phenomenology, classification of phase transitions. Mean field theories; Weiss theory, Landau theory, Van der Waals theory. Statistical mechanics of phase transitions; examples based on the Ising model. Introduction to scaling and the renormalisation group.
Classical mechanics: Calculus of variations. Hamilton's principle, Lagrangian formulation of classical mechanics, examples. Symmetry and conservation laws. Linear and nonlinear dynamics. Classical field theory. Nonlinear wave equations. 
Programme availability: 
PH40073 is Compulsory on the following programmes:Department of Physics
PH40073 is Optional on the following programmes:Department of Physics

Notes:
