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Symmetry Methods in Physics
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Module 11
Spontaneous Symmetry Breaking
1
Spontaneous vs. Explicit Symmetry Breaking
Define spontaneous symmetry breaking (SSB) and distinguish it from explicit symmetry breaking.
2
Spontaneous Symmetry Breaking: The Mexican Hat Potential
Demonstrate SSB in a scalar field theory with a "Mexican hat" potential.
3
Goldstone's Theorem: Proof and Implications
State and prove Goldstone's theorem relating broken continuous global symmetries to massless bosons.
4
Spontaneous Symmetry Breaking in Ferromagnets
Describe the spontaneous breaking of rotational symmetry in a ferromagnet as an example of SSB.
5
Spontaneous Symmetry Breaking in Superfluids & Superconductors
Describe the spontaneous breaking of global U(1) symmetry in a superfluid or superconductor.
6
The Abelian Higgs Mechanism
Demonstrate the Abelian Higgs mechanism, where a U(1) gauge boson acquires mass by absorbing a Goldstone boson.
7
The Higgs Mechanism in Electroweak Theory
Outline the Higgs mechanism in the context of the electroweak SU(2)xU(1) theory.
Landau Theory of Phase Transitions
Formulate the Landau theory of phase transitions using order parameters and symmetry considerations.
Previous module
Gauge Theories and Fundamental Symmetries
Next module
Topological Aspects of Symmetry and Matter