Quantum electrodynamics Lagrangian (QED Lagrangian)

L_{Q E D} = \overset{ˉ}{ψ} (i ℏ c D / - m c^{2}) ψ - \frac{1}{4 μ _{0}} F_{μ ν} F^{μ ν}

(1)

where:

$F$ is the electromagnetic tensor

Note that this is the sum of the:

Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
the electromagnetic interaction term $\frac{1}{4 μ _{0}} F_{μ ν} F^{μ ν}$ , which describes term describes forces

Note that the relationship between

ψ

and

F

is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore

F

As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):

by "Lagrangian" we mean Lagrangian density
the generalized coordinates of the Lagrangian are fields

Video 16.

Particle Physics is Founded on This Principle! by Physics with Elliot (2022)

Source.

Table of contents 326 1
- Derivation of the quantum electrodynamics Lagrangian (Derivation of the QED Lagrangian) Quantum electrodynamics Lagrangian 198

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QED Lagrangian