# Green’s Functions

• D. Ya. Petrina
Chapter
Part of the Mathematical Physics Studies book series (MPST, volume 17)

## Abstract

Consider a Hamiltonian of the system of particles interacting via a pair potential Φ and situated in the entire three-dimensional space ℝ3
$$H = {H_0} + {H_{\text{I}}} = \int {\psi {\text{*}}(x)} {\text{ }}\left( { - \frac{\Delta }{{2m}} - \mu } \right)\psi (x)dx + \frac{g}{2}\int {\psi {\text{*}}(x)\psi {\text{*}}(x\prime )\Phi (x{\text{ - }}x\prime )\psi (x\prime )\psi (x)dxdx\prime .}$$
(14.1)
Here, μ is a chemical potential, ψ*(x) and ψ(x) are operators of creation and annihilation independently of the type of statistics, and g is a coupling constant. Suppose that the frame of reference is chosen so that the lowest eigenvalue of the Hamiltonian is equal to zero
$$H{\Phi _0} = 0.$$
(14.2)
The eigenvector Φ0 that corresponds to the eigenvalue zero of the Hamiltonian H is called the ground state or “physical” vacuum.

## Keywords

Commutation Relation Thermodynamic Limit Evolution Operator Heisenberg Equation Wiener Measure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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