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Unformatted text preview: Homework Set No. 4, Physics 880.08 Deadline Wednesday, December 8, 2010 at NOON! 1. Time-ordered product of real scalar fields is defined by T ( x ) ( y ) = ( x y ) ( x ) ( y ) + ( y x ) ( y ) ( x ) , where s are operators in Heisenberg picture. a. (5 pts) In a free scalar field theory with mass m use Klein-Gordon equation along with the canonical commutation relations to show that [ 2 + m 2 ] T ( x ) ( y ) = i 4 ( x y ) where the derivative squared (the DAlembertian) is taken with respect to 4-coordinates x . b. (10 pts) Similar to what we did in class for retarded Green function, find an explicit expression for the Feynman propagator in coordinate space in a massless ( m = 0) theory by performing the following integral D F ( x y ) = integraldisplay d 4 k (2 ) 4 e i k ( x y ) i k 2 + i . Is Feynman propagator causal?...
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