hw22 - obtain is called the Yukawa potential.) 2. (10 pts)...

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Homework Set No. 2, Physics 880.02 Deadline – Thursday, May 7, 2009 1. (20 pts) Consider a theory of massive fermions ψ coupled to massive (real) scalar bosons ϕ with the Lagrangian L = ¯ ψ ( μ μ - M ) ψ + 1 2 μ ϕ ∂ μ ϕ - m 2 2 ϕ 2 - g ϕ ¯ ψ ψ. Assume that the fermions are much heavier than the bosons, M ± m . Calculate the static potential between a fermion and anti-fermion due to an exchange of a single boson Feld, similar to how we calculated the heavy quark potential in class. The fermion-boson vertex gives a factor of - ig . (This is Yukawa theory of nuclear interactions, with the fermions being protons and neutrons and the scalar particle being the pion. The potential you should
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Unformatted text preview: obtain is called the Yukawa potential.) 2. (10 pts) Now consider QED with massive photons: L = ( i D -M ) -1 4 F F + m 2 2 A A . Assuming again that fermions (electrons) are much heavier than the photons, M m , calculate the static electron-positron potential due to an exchange of a single photon. (Hint: the calculation should be similar to that of problem 1.) Note the dierence between your result and the Coulomb potential. 1...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.02 taught by Professor Kovchegov during the Winter '09 term at Ohio State.

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