finalA - UNIVERSITY OF CALIFORNIA SANTA BARBARA Department of Physics Physics 221A Prof Joe Polchinski http\/www.kitp.ucsb.edu\/~joep\/Web221A\/221A.html

finalA - UNIVERSITY OF CALIFORNIA SANTA BARBARA Department...

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UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Physics Physics 221A Quantum Field Theory Fall 2007 Prof: Joe Polchinski [email protected] FINAL EXAM Open notes, homework, solutions, Srednicki (the text, not the person). Please do not discuss the test with anyone but me before the due time. I will check my email regularly, and post any corrections/clarifications on the course web page. Begin: Tuesday, Dec. 11, noon. Due: Wednesday, Dec. 12, noon in my office, KITP 2319 (except for those who have made other arrangements). 1. Consider a theory ind= 4 with three real scalar fieldsA,B, andC, and the followingLagrangian density:L=12(μA∂μA+μB∂μB+μC∂μC+m2AA2+m2BB2+m2CC2)g2AB2h2CB2.There might be other terms inLbut you won’t need them (in particular you won’t needcounterterms).a) Write the Feynman rules for this theory (propagators and vertices).b) Consider first the casemA>2mB. What is the tree level decay rateAB+B?c) Now consider the casemA<2m
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