as1-2 - Physics 253b Assignment#1-2 updated February 8 2010...

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Unformatted text preview: Physics 253b Assignment #1-2 updated February 8, 2010 This is what I hope will be an easy a followup on last weeks problem that will get you thinking about the background field method. Do the that last part using the background field method and look at the discuss in the Coleman-Weinberg paper referred to below. Note that I have put the missing term into (1-2-1.3) below. Assume (for simplicity) m 1 = m 3 and show how the result you obtained last time arises from the expansion (in the coupling constants) of the Coleman-Weinberg contribution to the effective potential, 1 16 π 2 Tr m ( φ ) 4 log m ( φ ) 2 (1) The point is that since we are interested in a term with no derivatives, we can treat the background fields as constants and calculate the masses of the quantum fields φ 1 and φ 3 as functions of the parameters and the background fields φ b 2 and φ b 4 . I think that the easiest way to do this will be to break the complex φ 1 and φ 3 field up into real fields (because otherwise you will have to keep careful track of arrows). I really want this problem to be easy and to deepen your understanding of the background field method. I will talk more about this in class, but please ask questions as they occur to you....
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This note was uploaded on 02/04/2012 for the course PHY 253B taught by Professor Georgi during the Spring '10 term at Princeton.

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as1-2 - Physics 253b Assignment#1-2 updated February 8 2010...

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