Lecture 22: Quantum Electrodynamics | Summary and Q&A

TL;DR

QED is a theory that describes the interaction between photons and charged particles, such as electrons. It is based on the principles of gauge invariance and local symmetries.

Key Insights

• 🧑‍🤝‍🧑 QED is a theory that couples fermions to photons through a conserved current, providing a mathematical framework to describe the interaction between charged particles and electromagnetic fields.
• 🚨 The gauge invariance in QED emerges as a deep dynamical principle determining the interactions in the theory and applying to all fundamental interactions in nature.
• 🏑 The coupling of fermions and scalar fields to photons follows similar principles, but the inclusion of scalar fields requires the introduction of a covariant derivative to maintain gauge invariance.
• 🖐️ Gauge invariance plays a crucial role in removing unphysical degrees of freedom in the electromagnetic field and ensuring the consistency of the theory.

Transcript

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Questions & Answers

Q: What provides the conserved current J_mu in QED?

The conserved current J_mu in QED is provided by the fermionic fields, such as electrons. The U1 global symmetry associated with these fields leads to the conservation of the current.

Q: How does the coupling constant e in QED affect the interaction strength between fermions and photons?

The coupling constant e in QED determines the strength of the interaction between fermions and photons. A larger e value corresponds to a stronger coupling between the two particles.

Q: Why do different particles have different charges in QED?

In QED, different particles can have different charges because the coupling constant e can be arbitrary. The charge is determined by the relationship between the coupling constant and the Noether current.

Q: Can the e in QED be considered as a unit of charge?

Yes, the coupling constant e can be considered as a unit of charge. This interpretation arises because a change in the constant does not affect the conservation of the Noether current, determining the unit of charge.

Summary & Key Takeaways

• QED is derived from the Maxwell's equations, which describe the behavior of electromagnetic fields.

• It couples photons, represented by the vector field A_mu, to charged particles, such as electrons or fermions.

• The Lagrangian density for QED includes a term that represents the interaction between the fermions and the photons.