582-2008-2 - Physics 582, Fall Semester 2008 Professor...

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Unformatted text preview: Physics 582, Fall Semester 2008 Professor Eduardo Fradkin Problem Set No. 2: Symmetries and Conservation Laws Due Date: September 26, 2008 Here you will look again at problem 2 of problem set No. 1 in which you studied some of the properties of the dynamics of a charged ( complex) scalar field φ ( x ) coupled to the electromagnetic field A μ ( x ). Recall that the Lagrangian density L for this system is L = ( D μ φ ( x )) ∗ ( D μ φ ( x ))- m 2 | φ ( x ) | 2- λ 4! ( | φ ( x ) | 2 ) 2- 1 4 F μν F μν (1) where D μ is the covariant derivative D μ ≡ ∂ μ + ieA μ (2) e is the electric charge and ∗ denotes complex conjugation. 1. Derive an expression for the locally conserved current j μ ( x ), associated with the global symmetry φ ( x ) → φ ′ ( x ) = e iθ φ ( x ) φ ∗ ( x ) → φ ′∗ ( x ) = e − iθ φ ∗ ( x ) A μ ( x ) → A ′ μ ( x ) = A μ ( x ) (3) in terms of the fields of the theory....
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This note was uploaded on 09/20/2010 for the course PHYS 582 taught by Professor Leigh during the Fall '08 term at University of Illinois, Urbana Champaign.

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582-2008-2 - Physics 582, Fall Semester 2008 Professor...

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