Question

I am trying to calculate the following 2-point correlation function in standard QFT

⟨F_μν(x)F_αβ(y)⟩

As far as I know, I should expand Fμν in terms of the gauge fields Aμ (with the possibility of being non-abelian) and calculate the correlation function between them, right? The calculations are a mess (specially in the non-abelian case), so my question is: Is there a straightforward way of doing this in terms of diagrams? Or, if not by diagrams, is there any kind of shortcut?

Answer 1

Yes, there is a convenient and powerful tool in QFT called Feynman diagrams, which can simplify the calculations and provide a shortcut for calculating the 2-point correlation function ⟨F_μν(x)F_αβ(y)⟩. Feynman diagrams are graphical representations of particle interactions that allow physicists to visualize and compute the correlation functions.

Step-by-step explanation:

In quantum field theory (QFT), calculating the 2-point correlation function ⟨F_mu_nu(x)F_alpha_beta(y)⟩ involves expanding F_mu_nu in terms of the gauge fields A_mu and calculating the correlation function between them. This can be a messy calculation, especially in the non-abelian case.

However, there is a convenient and powerful tool in QFT called Feynman diagrams, which can simplify the calculations and provide a shortcut. Feynman diagrams are graphical representations of particle interactions that can be used to calculate the strengths and probabilities of interactions.

By assigning different symbols to different particles and representing their interactions in space-time, Feynman diagrams allow physicists to visualize and compute the correlation functions. These diagrams provide a more intuitive and efficient way to calculate the 2-point correlation function, especially in complex cases like non-abelian gauge theories.