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Unformatted text preview: 253a/Schwartz Due September 21, 2010 Problem Set 2 Problems marked with a * are optional, but strongly recommended. 1. Dimensional analysis. a) A photon coupled to a complex scalar field in D-dimensions has action S = integraldisplay d D x bracketleftbigg- 1 4 F 2- square + gA + 3 + bracketrightbigg (1) where F = ( A - A ) and square = as always but now = 0 , 1 , , D- 1 . What is are the mass dimensions of A , , g and (as functions of D )? b) An interaction is said to be renormalizable if its coupling constant is dimensionless. In what dimension D is the electromagnetic interaction renormalizable? How about the 3 interaction? 2. Is the transformation Y : ( t, x, y, z ) ( t, x,- y, z ) a Lorentz transformation? If so, why isnt it consid- ered with P and T as a discrete Lorentz transformation? If not, why not?...
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