as8 - Physics 253b Assignment#8 updated Monday 19 th April...

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Unformatted text preview: Physics 253b Assignment #8 updated Monday 19 th April, 2010, 07:25 Do the problem below. Make sure that you follow the rules of coherence. Typeset your solution in L A T E X file, zip your latex file and any nonstandard input files and/or packages necessary to compile it along with the pdf file it generates and submit the zip file to the appropriate drop box on the web page. 8-1 . On this set we are going to explore Weinberg’s second model of lepton that discussed in class. To begin let’s briefly discuss charge conjugation. The charge conjugation matrix is defined by C 2 = I C = C † C ( γ μ ) * C =- γ μ (8-1.1) The precise form of C depends on the representation of the γ matrixes (for example you can use the so-called Majorana basis in which all the γ s are imaginary, in which case C = I ). Show for a given fixed basis for the γ μ s, that C is unique up to a sign. 8-2 . Consider a variant of Weinberg’s SU (3) model of leptons in which the e and μ fields transform like two SU (3) triplets, as follows: ψ e L = ν e e- e + L ψ μ L = ν μ μ- μ + L (8-2.1) As discussed in class, assume that there is a field ξ that breaks SU (3) down to SU (2) × U (1) , h | ξ | i ≈ u u- 2 u for u v (8-2.2) More specifically, the transformation properties of the fermion fields and...
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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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as8 - Physics 253b Assignment#8 updated Monday 19 th April...

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