Quantum field theory Exercises 4.
2005-11-21
•Exercise 4.1.
Consider a massive particle moving with velocityv=tanhη.
• Show that, ifE is the energy of the particle and p its momentum along the propogation direction, then
η= 1
2logE+p E−p.
• Verify that under a boost in the direction of motion of the particle with velocityv0 (and corresponding rapidityη0=arctanhv0)ηtransforms additively
η→η+η0.
•Exercise 4.2.
Prove that, ifψR andξRare right-handed Weyl spinors,ξR†σµψR is a four-vector, and simi- larly forξL†σ¯µψL, whereξL,ψL are left-handed Weyl spinors.
•Exercise 4.3.
Find the explicit form of the variation of an antisymmetric tensorFµ ν under an infinites- imal Lorentz transformation. Writing F0i =−Ei and Fi j = −εi jkBk, find the infinitesimal transformation ofEiandBi.
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