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Unformatted text preview: Homework Set No. 1, Physics 880.08 Deadline Monday, October 18, 2010 1. Consider a real scalar interacting field theory with the Lagrangian density L = 1 2 - m 2 2 2- 3! 3 where is a real number. (a) (5 pts) Construct Euler-Lagrange equation for this theory. (b) (5 pts) Find the energy-momentum tensor T for this theory and show explicitly that it is conserved, T = 0, for the fields satisfying Euler-Lagrange equation found in part (a). 2. The Lagrangian density for a two-component complex scalar field vector = parenleftbigg 1 2 parenrightbigg is given by L = vector vector - m 2 vector vector where Hermitean conjugation is defined by vector = ( 1 , 2 ) . (a) (3 pts) Show that the above Lagrangian is invariant under the following global SU (2) symmetry i i = parenleftbigg exp braceleftbigg i vector vector 2 bracerightbiggparenrightbigg ij j with vector...
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