If the gas is not a zero kelvin there will be Doppler broadening.
http://www.phy.ohiou.edu/~mboett/astro401_fall12/broadening.pdf
So the answer to your first question is in some part yes.
Quantum Field Theory for the Gifted Amateur by Lancaster and Blundell doesn’t have the 1/2, which is interesting! In that text the factors only appear when calculating the wave-function. So something is wrong with one of them...
Great thanks for confirming that. So wouldn’t you need four operators for 2 particles? Two to annihilate the two original states and two to create the new ones?
You might have less consternation if you considered polarisation. The |H> and |V> states are clearly orthogonal and any other vector might be built from a sum of the two. However with spin the states of up and down states are orthogonal so it’s more tricky to picture.
For me, as I see it, the model breaks down at assumption 5. This assumption is written into agree with experimental results. But it explicitly states that B is a function of gamma. Given that gamma is dependent on the orientation of P1 this implies that B depends on said orientation. This is a...
You state that
“It is assumed that a photon can be simultaneously in different p-states depending on the value of a parameter λ and a chosen direction relative to the polarization of the photon. That means some of the photons with polarization α are also in p-state β and thus pass a polarizer...