# Green's Functions and Feynman Diagrams

• rolotomassi
In summary, the conversation discusses Greens functions and their role in obtaining a perturbation series and Feynman diagrams in quantum field theory. Virtual particles, which are a consequence of the perturbation series, are represented in Feynman diagrams as internal legs and are involved in the emission and absorption of particles. These virtual particles are not physically real, but rather a mathematical tool used in the perturbation series.
rolotomassi
I've been learning about Greens functions. I'm familiar with how to find them for different differential operators and situations but far from fully understanding them. We were shown in lecture how they can be used to obtain a perturbation series, leading to Feynman diagrams which represent them. But there was no mention about virtual particles which is what I thought closely related to Feynman diagrams. You include all of the ways a particle and emit, re-absorb and do whatever with the virtual particles and the more events you include the more terms in the series and the more accurate etc..

Do virtual particles arise as a mathematical consequence of Greens function then, and if so how?

Yes, all of the lines in a diagram which correspond to particles whose energy and momentum don't fulfill ##E^2=m^2c^4+p^2c^2## are virtual particles (one says also "off the mass shell").
This doesn't mean that virtual particles really exist, rather, they are a consequence of the perturbation series one is using.

In the perturbation series for quantum field theory, each term can be represented by a Feynman diagram. These diagrams consist of external legs, internal legs, and vertices. The external legs represent initial- and final-state particles. The internal legs stand for Green's functions of the differential operators corresponding to the equations of motion of particles. These Green's functions can be thought of as giving the amplitude for a particle to propagate from one place to another. So we call the internal legs "virtual particles" and we think of the vertices as representing the emission or absorption of particles.

Thanks a lot. Big help

## What is the purpose of Green's Functions and Feynman Diagrams?

The purpose of Green's Functions and Feynman Diagrams is to provide a mathematical framework for studying and understanding the behavior of quantum mechanical systems. They are commonly used in theoretical physics to describe the interactions between particles and their resulting effects.

## What is a Green's Function?

A Green's Function is a mathematical function that describes the response of a system to a specific input. In the context of quantum mechanics, it represents the probability amplitude for a particle to move from one point to another in a given amount of time, taking into account all possible paths between the two points.

## What are Feynman Diagrams?

Feynman Diagrams are graphical representations of mathematical expressions that describe the interactions between particles in a quantum mechanical system. They were developed by physicist Richard Feynman as a way to visualize and calculate complex particle interactions.

## How are Green's Functions and Feynman Diagrams related?

Green's Functions and Feynman Diagrams are closely related, as they both provide mathematical tools for understanding and calculating quantum mechanical systems. Green's Functions are used to calculate the amplitudes in Feynman Diagrams, which in turn provide a graphical representation of the mathematical expressions.

## What are some applications of Green's Functions and Feynman Diagrams?

Green's Functions and Feynman Diagrams have a wide range of applications in physics, including in quantum field theory, condensed matter physics, and nuclear physics. They are also used in chemistry and engineering to study the behavior of complex systems. Additionally, they have been used in the development of technologies such as transistors and superconductors.

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