Derivation of the one-particle Green's function?

In summary, the individual is seeking a detailed derivation of the single particle Green's function and is looking for a reference book that covers this topic. They have not been able to find it in books by Sakurai, Ashcroft, or Jackson, and are specifically interested in a quantum text with bracket notation. The recommended text for this topic is Bjorken and Drell vol II, Appendix C.
  • #1
gluons
15
0
Hello,

I am looking for a good reference book that has a detailed derivation of the single particle Green's function. I expected this to be in Sakurai but it's not. I couldn't find the spectral representation of this simple function in Ashcroft or any other solid state book either. Jackson has plenty on Green's functions for charged systems but I'd like to use a quantum text with bracket notation of some kind.

Basically I am looking for some thorough treatment of the resolvent of the single particle Hamiltonian and the representations of the Green's function. What text would you recommend?
 
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  • #2
Assuming you mean the Green's functions for the Klein-Gordon equation and the Dirac equation, a good treatment can be found in Bjorken and Drell vol II, Appendix C.
 

FAQ: Derivation of the one-particle Green's function?

What is the one-particle Green's function?

The one-particle Green's function is a mathematical tool used in quantum mechanics to describe the behavior of a single particle in a system. It is a function that relates the initial state of a particle to its final state, taking into account all possible paths the particle can take.

What is the significance of the one-particle Green's function?

The one-particle Green's function is significant in many areas of physics, including condensed matter, nuclear physics, and quantum field theory. It allows for the calculation of important physical quantities, such as the density of states and the spectral function.

How is the one-particle Green's function derived?

The one-particle Green's function is derived using the Feynman path integral formalism, which involves summing over all possible paths a particle can take. This leads to an integral equation that can be solved to obtain the Green's function.

What is the role of the one-particle Green's function in many-body systems?

In many-body systems, the one-particle Green's function is used to understand the behavior of a single particle in the presence of other particles. It provides information about the interactions between particles and allows for the calculation of physical quantities, such as correlation functions.

How is the one-particle Green's function related to other Green's functions?

The one-particle Green's function is a special case of the many-particle Green's function, which describes the behavior of multiple particles in a system. Additionally, the one-particle Green's function is related to the self-energy function, which accounts for the effects of interactions between particles.

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