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
