Quantum Field Theory

It is the study of quantum fields.

Intro 1

According to this video:
QFT is a cool version of ∞-dim calculus

f(x)=?f(x0)+f′(x0)(x−x0)+12f″(x0)(x−x0)2+…classical field theory⏟first termsemi-classical field theory⏟higher-order termsperturbative quantum field theory⏟all terms combined∃f(x)with given Taylor expansion? : non-perturbative QFT

Intro 2

From this eigenchris video. It is the best introduction to Quantum Field Theory I have found for the moment.
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Lagrangian point of view

Steps:

  1. Lagrangian mechanics for a particle
  2. Lagrangian mechanics for several particles: see Lagrangian Mechanics
  3. Lagrangian mechanic for a classical field: see Lagrangian field theory
  4. Feynman approach to QM for a particle.
  5. Feynman approach to fields... See also Feynman's path integral formulation.

Hamiltonian point of view

Quantum Mechanics for particles can be approached from Lagrangian Mechanics (Feynman) or Hamiltonian mechanics (I should review my old notes, starting from here). If we apply the "link" of Hamiltonian mechanics to Quantum mechanics to fields (Hamiltonian field theory) instead of particles, we obtain Quantum Field Theory.