Green function for KG equation

Thread starter paweld
Start date May 14, 2010
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Function Green Green function

In summary, A Green function for the KG equation is a mathematical tool used to solve the KG equation, which is a second-order partial differential equation that describes the behavior of scalar fields in physics. It is derived by solving the KG equation with a delta function as the source term using Fourier transforms and other mathematical techniques. The Green function has a physical interpretation as the amplitude of the field due to a point source and is used in various practical applications such as in quantum field theory and cosmology. It has important properties, including linearity, translation invariance, and a causal structure.

May 14, 2010

paweld

There exists very simple formula for Green function for wave equation:
[tex] G(t,x,t',x') = \delta (t-t'\pm \frac{|x-x'|}{c})/|x-x'| [/tex].
I wonder whether there exist similar formula for Green function
for Klein-Gordon equation (with mass >0) for any boundary condition.

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May 14, 2010

madness

I think it's just the Feynman propagator (http://en.wikipedia.org/wiki/Propagator#Feynman_propagator)

Related to Green function for KG equation

1. What is a Green function for the KG equation?

A Green function for the KG (Klein-Gordon) equation is a mathematical tool used to solve the KG equation, which is a second-order partial differential equation that describes the behavior of scalar fields in physics. It represents the response of the system to a point source or "delta function" input.

2. How is the Green function for the KG equation derived?

The Green function for the KG equation is derived by solving the KG equation with a delta function as the source term. This results in an integral equation that can be solved to obtain the Green function. The derivation process involves using Fourier transforms and other mathematical techniques.

3. What is the physical significance of the Green function for the KG equation?

The Green function for the KG equation has a physical interpretation as the amplitude of the field at a point in space and time due to a point source located at another point in space and time. It is used to calculate the behavior of scalar fields in various physical systems, such as in quantum field theory and cosmology.

4. How is the Green function for the KG equation used in practical applications?

The Green function for the KG equation is used in various practical applications, such as in solving boundary value problems in physics, calculating scattering processes, and modeling the behavior of fields in different physical systems. It is also used in theoretical studies of quantum field theory and cosmology.

5. What are the properties of the Green function for the KG equation?

The Green function for the KG equation has several important properties, including linearity, translation invariance, and symmetry. It also satisfies the differential equation for the KG equation, and its Fourier transform can be used to obtain the spectral representation of the field. Additionally, it has a causal structure, meaning that it only depends on past events and not future ones.