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Having difficulty comprehending a problem in Peskin's text

  1. Dec 14, 2011 #1
    In his "an introduction to quantum field theory", problem 5.4 (c), he describes a bound state of positronium as [tex]|B(k)\rangle=\sqrt{2M}\int{\frac{d^{3}p}{(2\pi)^{3}}\psi_{i}(p)a^{\dagger}_{p+\frac{k}{2}}\Sigma^{i}b^{\dagger}_{-p+\frac{k}{2}}|0\rangle}[/tex]
    where [itex]\psi_{i}(p)[/itex] are the p-orbtal wavefunctions in momentum space(i=1,2,3), [itex]a^{\dagger}[/itex]and [itex]b^{\dagger}[/itex] are electron and positron creation operator, [itex]\Sigma^{i}[/itex] is some 2 by 2 matrix. I don't understand where this [itex]\Sigma^{i}[/itex] comes from. LHS of the equation is just a ket, in this case shouldn't RHS be a superposition of kets? What should I make of [itex]\Sigma^{i}[/itex]?
     
  2. jcsd
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