# ps4 - Princeton University Physics 509 Quantum Field Theory...

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Princeton University Physics 509 Quantum Field Theory Problem Set 4 14 — Particle creation by a classical source Do problem 4.1 in Peskin and Schroeder. 15 — Two-body decay Suppose that particle 1 decays into several other particles 1 2 + 3 + 4 + ··· + n. The decay rate d Γ is given by Fermi’s golden rule , dΓ = |M| 2 S 2 m 1 d Π d Π = ± d 3 p 2 (2 π ) 3 2 E 2 ² ··· ± d 3 p n (2 π ) 3 2 E n ² × (2 π ) 4 δ 4 ( p 1 - P f ) . where M is the reduced matrix element and P f = n 2 p i is the sum of the 4-momenta of the outgoing particles. The delta function enforces conservation of energy and momentum. The decaying particle is presumed to be at rest, p 1 = ( m 1 , 0 ). Here, S is a product of symmetry factors: 1 /j ! for each group of j identical particles in the ﬁnal state. Consider now the special case of a two-body decay, in which the outgoing particles carry masses m 2 and m 3 . In the following we are going to calculate the decay rate, assuming that the scattering amplitude M is given. It can actually be calculated and we will do so in the next exercise. We want to integrate the right-handside over all outgoing momenta. To this end, use the delta function to do the

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## This note was uploaded on 02/02/2012 for the course PHY 509 taught by Professor Alexanderm.polyakov during the Fall '09 term at Princeton.

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ps4 - Princeton University Physics 509 Quantum Field Theory...

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