IFT

First, why Field Theory?

• We need a consistent quantum treatment of relativistic particles.
• Our theory should be local and causal (since nature is).
• Our theory should allow for a dynamical number of particles.

With a QFT (Quantum …), we can treat all particles on the same footing, with a common framework (spin-statistics relation emerges). It becomes the language to formulate our most fundamental theory of nature. It also supports a consistent, low energy theory for quantum gravity (our next to last theory).

But, how do we build a QFT?

1. Dynamics: Review Lagrangian and Hamiltonian mechanics and apply it to fields.
2. Quantise: Implement canonical commutation relations.
3. Interpret: Introduce Fock Space and identify familiar operators.

Before delving, check Conventions

Topics:

• Classical Mechanics Review
• Quantisation
• Symmetry 1
• index
• Interactions and the Perturbative Expansion
• Fermions 1