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Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title QUANTUM FIELD THEORY
Code MATH425
Coordinator Dr J Smirnov
Mathematical Sciences
Juri.Smirnov@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 M Level First Semester 15

Aims

To provide a broad understanding of the essentials of quantum field theory.

Learning Outcomes

(LO1) Explain the connections to classical field theory, the concept of an internal symmetry and the relation between symmetries and conserved quantities.

(LO2) Apply the rules of the harmonic oscillator to derive the spectrum of the theory, as well as describing a driven system with different in and out states.

(LO3) Understand the connection between the time-evolution of the quantum system and the perturbative formulation of the scattering amplitude.

(LO4) Evaluate amplitudes in perturbation theory using the Wick theorem and understanding the connection to Feynman diagrams.

(LO5) Compute Amplitudes using the Feynman diagram technique.

(LO6) Calculate scattering and decay rates based on the computed amplitudes, feeding into matrix elements.

(LO7) Apply the principles behind regularisation and renormalisation to some models.

Syllabus
 

Review of classical field theory (2 lectures)
Klein-Gordon equation (2 lectures)
Dirac equation; plane wave solutions (4 lectures)
Quantisation of free scalar field (6 lectures)
Quantisation of Dirac field (4 lectures)
Interacting fields; the S-matrix (4 lectures)
Feynman rules for scalars and fermions (4 lectures)
Calculation of cross-sections (4 lectures)
Divergences and renormalisation (6 lectures)

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment  90    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 3  0    20       
Homework 1  0    20       
Homework 2  0    10