spinor yi vector Am perturbation provability Wicks theorem
spinor yi vector Am perturbation provability Wick's theorem locality, Lorentz inv. gauge inv. interaction reprensatation S-matrix
provability S-matrix
electron quark scattering k' provability P? k =provability amplitude p (p'≠p, k'≠k) Let us consider electron quark scattering. We want to know the provability. For this purpose, we calculate the provability amplitude. p'
p = p' =0 bbe†b† q†〉 〉 q = = 〈= = ∴ 0 k' electron p'≠p, k'≠k quark scattering provability P? k† = † abbreviations 〈bq'be' beamplitude bq 〉= 0 〈bq'be'† =provability be' be b' =
k' electron quark scattering provability P? k = =provability amplitude expand square 〈b'qb'e p'≠p ∴ 0 = p p' k'≠k ∴ 0 = abbreviations ' n 'n ' = = An (x ') ' be†bq†〉 yq(x ')
electron quark scattering k' provability P? k =provability amplitude Wick's theorem p p'
electron quark scattering k' provability P? k =provability amplitude p p'
=provability amplitude
q 1 = q q = k' - k q k' - k = k' - k q = = T : T-matrix
= Feynman rules = T : T-matrix
内線 internal line photon fermion vertex 外線 external line 粒子 particle outgoing incoming 反粒子 antparticle loop fermion loop T matrix
loop diagram
loop diagram
Feynman rules
scattering cross section reaction a 1+a 2→a 3+a 4 momentum mass Ns # of scatterings s target cross section N 1 # of projectiles N 2 # of targets energy A area scattering provability volume of space total time flux
reaction 反応 s-channel t-channel u-channel invariant variables 不変変数 t-channel time s-channel laboratory frame 実験室系 center-of-mass frame 重心系
center-of-mass frame laboratory frame
decay width G =decay provability/total time = # of decays/ # of particles /total time # of decays # of particles total time
center-of-mass frame
fermion scattering k' k p p'
scattering cross section 散乱断面積 differential scattering cross section 微分断面積
scattering cross section 散乱断面積 differential scattering cross section 微分散乱断面積 unpolarized scattering cross section 非偏極散乱断面積 ni : # of sipn states of particle ai (massive particle) (massless particle) ji : spin quantum #
- Slides: 37