PS2 - 253a/Schwartz Due Problem Set 2 Problems marked with...

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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 μν 2- φ ⋆ square φ + gA μ φ ⋆ ∂ μ φ + λφ 3 + bracketrightbigg (1) where F μν = ( ∂ μ A ν- ∂ ν A μ ) and square = ∂ μ ∂ μ as always but now μ = 0 , 1 , , D- 1 . What is are the mass dimensions of A μ , φ, g and λ (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 φ 3 interaction? 2. Is the transformation Y : ( t, x, y, z ) → ( t, x,- y, z ) a Lorentz transformation? If so, why isn’t it consid- ered with P and T as a discrete Lorentz transformation? If not, why not?...
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PS2 - 253a/Schwartz Due Problem Set 2 Problems marked with...

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