# Scattering Amplitudes for Phi 4 Theory

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• Diracobama2181
In summary, the conversation discusses the meaning of 1 loop order in the context of scattering matrix elements and Feynman diagrams. It is explained that 1 loop refers to the first order expansion of the scattering matrix element, which involves the integration of four scalar fields. The conversation concludes with the realization that a second order expansion, involving the integration of eight scalar fields, would be needed to reach the $$\lambda^2$$ term.
Diracobama2181
TL;DR Summary
How do if calculate ##i\mathcal{M}(\vec{ k_1}\vec{ k_2}\rightarrow \vec{ p_1}\vec{ p_2})(2\pi)^4\delta^{ (4)}(p_1 +p_2-k_1-k_2)## to 1 loop order?
I know $$i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2)$$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element $$\bra{\vec{p_2}\vec{p_1}}\hat{S}\ket{\vec{k_1}\vec{k_2}}$$, would 1 loop just be the first order expansion ($$\frac{\lambda}{4!}\int d^4z\bra{\vec{p_1}\vec{p_2}}\phi\phi\phi\phi\ket{\vec{k_1}\vec{k_2}}$$) in this case?

Last edited:
Never mind. Figured it out. I would have to go to $$\lambda^2$$ in the expansion. Thanks.

vanhees71

## 1. What is the significance of "Scattering Amplitudes for Phi 4 Theory" in the field of physics?

The scattering amplitudes for phi 4 theory are important in understanding the interactions between particles in quantum field theory. They provide a way to calculate the probabilities of particles scattering off of each other, which is crucial in understanding the behavior of particles at the subatomic level.

## 2. How are scattering amplitudes for phi 4 theory calculated?

Scattering amplitudes for phi 4 theory are calculated using Feynman diagrams, which represent the different possible interactions between particles. These diagrams are then used to calculate the probabilities of different scattering events.

## 3. What is the relationship between scattering amplitudes for phi 4 theory and the Standard Model of particle physics?

The scattering amplitudes for phi 4 theory are a key component of the Standard Model, which is the most widely accepted theory for explaining the behavior of particles and their interactions. The phi 4 theory is a simplified version of the Standard Model, making it a useful tool for studying and understanding the more complex interactions in the Standard Model.

## 4. How do scattering amplitudes for phi 4 theory contribute to our understanding of the universe?

Scattering amplitudes for phi 4 theory provide a way to study and predict the behavior of particles at the subatomic level. This knowledge is crucial in understanding the fundamental forces and interactions that govern the universe. It also helps us to develop new technologies and make advancements in fields such as medicine and energy.

## 5. What are some current research topics related to scattering amplitudes for phi 4 theory?

Some current research topics related to scattering amplitudes for phi 4 theory include studying the effects of higher order corrections on the calculations, exploring the connections between phi 4 theory and other theories such as string theory, and investigating the implications of phi 4 theory for dark matter and dark energy. Researchers are also working on developing new techniques and methods for calculating scattering amplitudes in more complex systems.

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