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ps_1_2010

# ps_1_2010 - Euler-Lagrange equations unchanged[20pts 3 Use...

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Duke University Physics Department Physics 305 January 14, 2010 Assignment No. 1 (60 pts) (due in class Jan-26-2010) Problems: 1. [20 pts] The Lagrangian density for a vector field with mass M is written as: L = - 1 4 ( ν A μ - μ A ν )( ν A μ - μ A ν ) + 1 2 M 2 A μ A μ (1) Use the Euler-Lagrange equation to derive the Proca equation: ν ( ν A μ - μ A ν ) + M 2 A μ = 0 (2) Show Eqn. (2) can be written further as ( ν ν + M 2 ) A μ = 0 (3) 2. Verify explicitly that changing the Lagrangian density by a total divergence leaves the
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Unformatted text preview: Euler-Lagrange equations unchanged. [20pts] 3. Use the requirement that the Lagrangian be invariant under a continuous symmetry to deduce the conserved quantity that corresponds to a particular transformation. Show that invariant under (i) translations in space, (ii) translations in time, (iii) spatial rotations implies conservation of (i) momentum, (ii) energy, (iii) angular momentum. [20pts] 1...
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