# Vector field self-energy amplitude and imaginary part

+ 0 like - 0 dislike
400 views

Suppose we have some diagram $M(p)$ of self-energy of massless vector field (i.e., indeed the gauge field). Let's compute its imaginary part. Let's assume that we obtain
$$\text{Im}M(p) = c \times p^{4}\theta(p^{2}), \quad \text{where c is finite}$$

What does this mean?

asked Jan 10, 2017
edited Jan 10, 2017

Source of your formula?

@ArnoldNeumaier : I've found this result by computing the 6-th order self-energy diagram of the axial gauge field in the anomalous abelian gauge field theory. Precisely, its longitudinal part contains the imaginary part I'vr obtained. This result is connected with the anomaly, so I want to know what is the physical sense of it.

@ArnoldNeumaier : sorry, there is the mistake in the expression above. Instead of $M$ there must be $\text{Im}M$.

In general, an imaginary self-energy indicates (as in resonances) the inverse lifetime of an unstable state. One has it for example in the Lamb shift. I am not sure how to interpret it in a field theory.

@ArnoldNeumaier : indeed, this property stays in the quantum field theory due to optical theorem. However, this is connected to non-zero mass of decaying particle, while I don't understand whether the imaginary part above signals about the non-zero mass.

## Your answer

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverfl$\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.