Advanced Quantum Field Theory - Workspace

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Le Bellac, Quantum and Statistical Field. Theory. ○ Bailin & Love, Introduction to Gauge Field. Theory. ○ Srednicki, Quantum Field Theory. ○ Weinberg ...
Advanced Quantum Field Theory 2014-15

Lecturer Prof Arttu Rajantie  E-mail: [email protected]  Room H605  Tel 0207 5947835  Office hour: Tuesdays 12 o’clock 

Web page http://www.imperial.ac.uk/theoreticalphysics/msc/aqft

Lecture Notes Available on the web page  More details, but less explanation than lectures  Uploaded section by section  Full set available from last year 

Books 

Peskin&Schroeder: An Introduction to Quantum Field Theory (The core text for this course)

Books 

Zee, Quantum Field Theory in a Nutshell (Not a traditional textbook, but very useful background reading)

Books Le Bellac, Quantum and Statistical Field Theory  Bailin & Love, Introduction to Gauge Field Theory  Srednicki, Quantum Field Theory  Weinberg, Quantum Theory of Fields I& II 

Aims to understand how realistic quantum field theories can be quantised consistently  to acquire the necessary skills to calculate observables in these theories  to understand the physical meaning of renormalisation 

Non-Abelian Gauge Fields Standard Model: SU(3)xSU(2)xU(1) gauge symmetry  Strong, weak and electromagnetic interactions  Quantisation is hard 

Lorentz invariance?  Gauge invariance?  Divergences? 

Divergences Predictions all infinite?  Renormalisation: 

Subtract divergences?  Sweep divergences under carpet? 

Renormalisation 

“I must say that I am very dissatisfied with the situation, because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way.” (Paul Dirac 1975)

Renormalisation 

“The shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! … I suspect that renormalization is not mathematically legitimate.” (Richard Feynman, 1985)

Renormalisation 

Wilsonian approach (Kenneth Wilson, Nobel 1982):   



Effective theories Scale dependence Continuum limit Critical phenomena: Phase transitions

Non-Abelian Gauge Fields 

Renormalisation of EW theory (‘t Hooft and Veltman, Nobel 1999)

Non-Abelian Gauge Fields 

QCD: Asymptotic freedom (Gross, Politzer & Wilczek, Nobel 2004)

Outline Path Integrals

1. 

 

Operators → functional integrals Feynman rules Quantization of gauge fields

Renormalisation

2.    

UV divergences Renormalised perturbation theory Renormalisation group Renormalisation of non-Abelian gauge fields

Path Integrals 

Operators → Functional integrals

Lorentz invariant  Renormalisation easier to understand  Works for non-Abelian gauge fields 

Path Integrals: Heuristic Argument 

Double slit experiment

Path Integrals: Heuristic Argument 

Double slit experiment



Light emitted at S, detected at O

Path Integrals: Heuristic Argument 

Double slit experiment



Probability:



Superposition principle:

Path Integrals: Heuristic Argument 

Drill n holes



Probability:



Superposition principle:

Path Integrals: Heuristic Argument 

Add another wall



Probability:



Superposition principle:

Path Integrals: Heuristic Argument Infinite no of walls, infinite no of holes  Probability: 



Superposition principle: Sum over all paths