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UNIVERSITY OF CALIFORNIA, SANTA BARBARADepartment of PhysicsPhysics 221AQuantum Field TheoryFall 2007Prof: Joe Polchinski[email protected]FINAL EXAMOpen notes, homework, solutions, Srednicki (the text, not the person). Pleasedo not discuss the test with anyone but me before the due time. I will checkmy email regularly, and post any corrections/clarifications on the course webpage.Begin: Tuesday, Dec. 11, noon.Due: Wednesday, Dec. 12, noon in my office, KITP 2319 (except for those who have madeother 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)−g2AB2−h2CB2.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 rateA→B+B?c) Now consider the casemA<2m