- #1

ofer

- 3

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we are talking about an interacting theory of 2 complex scalar fields,

lets call them ψ1 and ψ2.

the interaction term is: Lint=λ(ψ2)^3(ψ1)

i have found the free propagator defined as:

Df-i(x-y)=<0|T(ψi(x) ψi*(y))|0> i=1,2.

what i am strugling with is that when considering the free parts

this propagator is 0 for <0|T(ψi ψi)|0> (no complex conjugate=no anti-particle).

and also it is 0 for <0|T(ψi ψj)|0> ,i≠j.

meaning that a field can only contract with it's conjugate counter part in the free theory.

so when i try to calculate an interaction corelator in 1st order of different forms i get 0, for instantce:

<Ω|T(ψ1 ψ2*)|Ω>

this term turns out 0 because there is no one to contract with all the none-conjugate fields

in the interaction hamiltonian.

am i miss understanding things here,

or is the first corelator to be none-zero in this picture of the form:

<Ω|T(ψ2* ψ2* ψ2* ψ1* )|Ω> ??

help will be much apriciated.

thank you.