# Two loop Feynman diagram with quartic vertex

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In summary: Once you have these, you can verify the coefficients in the paper by Becker and Becker. In summary, the conversation discusses the calculation of the effective potential of two D0 branes scattering in Matrix theory and verifying the coefficients in a specific paper. The approach involves expanding the fields around a background classical field and evaluating diagrams without legs. The contribution to the effective action is then determined by calculating the propagators for the fields.
TL;DR Summary
I want to calculate a feynman diagram with four fields and two loops
I am trying to calculate the effective potential of two D0 branes scattering in Matrix theory and verify the coefficients in this paper: K. Becker and M. Becker, "A two-loop test of M(atrix) theory", Nucl. Phys. B 506 (1997) 48-60, arXiv:hep-th/9705091. The fields are expanded about a constant background classical field which is treated non perturbatively. As a consequence, the diagrams have no legs and we can calculate the effective action just by evaluating the diagrams.

I need to know if I am following the correct approach, especially because the calculations are tedious and I need to prove a cancellation at the end. Consider the quartic vertex, where the wavy lines indicate bosonic and gauge field propagators.This diagram corresponds to the quartic vertex $$-\frac{g}{2}\epsilon^{abx} \epsilon^{cdx} A_{a} Y^{i}_{b}A_{c} Y^{i}_{d}$$

−g2ϵabxϵcdxAaYbiAcYdi in a Lagrangian expanded around a background field. We know the Feynman rules for the theory, i.e. we know $<AA>, <YY> \text{ and } <YA>$ propagators. I need to know if the contribution to the effective action is correct: $$-\frac{g}{2} \epsilon^{abx} \epsilon^{cdx}\int d\tau \langle A_{a} A_{c} \rangle \langle Y^{i}_{b} Y^{i}_{d} \rangle + \langle A_{a} Y^{i}_{b} \rangle \langle A_{c} Y^{i}_{d} \rangle$$
\langleYY⟩,\langleAA

⟩,\text{ and }\langleAY⟩ propagators. I need to know if the contribution to the effective action is correct:−g2ϵabxϵcdx∫dτ⟨AaAc⟩⟨YbiYdi⟩+⟨AaYbi⟩⟨AcYdi⟩Yes, your approach is correct. The contribution to the effective action is indeed given by the expression that you have written. The only thing that you need to do is to calculate the propagators for the fields in order to obtain the numerical factors that you need to complete the calculation.

## 1. What is a two loop Feynman diagram with quartic vertex?

A two loop Feynman diagram with quartic vertex is a graphical representation used in theoretical physics to calculate the probability of particle interactions. It involves two loops, or closed paths, and a quartic vertex, which is a point where four particles come together and interact.

## 2. How is a two loop Feynman diagram with quartic vertex calculated?

To calculate a two loop Feynman diagram with quartic vertex, one must use Feynman rules, which assign mathematical expressions to each component of the diagram. These rules involve integrating over all possible momentum values and applying conservation laws to determine the overall probability of the interaction.

## 3. What is the significance of a two loop Feynman diagram with quartic vertex?

A two loop Feynman diagram with quartic vertex is significant because it represents a higher order correction to a particle interaction. It takes into account more complex interactions and can provide more precise calculations for certain physical phenomena.

## 4. How does a two loop Feynman diagram with quartic vertex relate to quantum field theory?

In quantum field theory, particles are described as excitations of underlying quantum fields. The two loop Feynman diagram with quartic vertex represents a specific way in which these particles can interact within the framework of quantum field theory.

## 5. What are some real-world applications of a two loop Feynman diagram with quartic vertex?

A two loop Feynman diagram with quartic vertex has applications in many areas of physics, including particle physics, condensed matter physics, and cosmology. It is used to calculate the probability of various particle interactions and can help provide insight into the behavior of particles and the fundamental forces of nature.

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