Skip to main content
grasp.study
About
Explore
Pricing
Log in
Try it for free
Back to course
👋
Welcome to a Grasp lesson
Create a free account
to keep studying and create your own study path.
Symmetry Methods in Physics
·
Module 9
Noether's Theorem and Gauge Symmetries
1
Noether's Theorem for Classical Mechanics
State and prove Noether's theorem for classical mechanical systems with continuous symmetries.
2
Noether's Theorem in Classical Mechanics
Derive conservation of energy, momentum, and angular momentum from spacetime symmetries in classical mechanics.
3
Noether's Theorem in Classical Field Theory
Extend Noether's theorem to classical field theories and derive the corresponding conserved currents.
4
Noether's Theorem and the Energy-Momentum Tensor
Derive the energy-momentum tensor from the translational invariance of a Lagrangian density.
5
Global vs. Local Symmetries: The Principle of Gauge Invariance
Distinguish between global and local (gauge) symmetries and motivate the principle of local gauge invariance.
6
Gauge Fields and Covariant Derivatives from Local U(1) Invariance
Derive the gauge field and covariant derivative from the requirement of local U(1) gauge invariance.
7
From Global to Local: Deriving the QED Interaction from Dirac Theory
Show that imposing local U(1) gauge invariance on the Dirac Lagrangian generates the QED interaction term.
8
Ward-Takahashi Identity from U(1) Symmetry
Derive the Ward-Takahashi identity from global U(1) symmetry in quantum field theory.
Previous module
Symmetries in Crystalline Solids
Next module
Gauge Theories and Fundamental Symmetries