Generating functions for canonical systems of fermions

Area of Science:

• Quantum mechanics
• Many-body physics
• Computational physics

Background:

• Pratt's method uses diagrammatic techniques for degenerate fermion systems.
• This method is efficient but assumes no explicit two-body interactions.
• It allows for the inclusion of conservation laws with low computational cost.

Purpose of the Study:

• To explore an alternative method for deriving recursion relations for degenerate fermions.
• To investigate if recursion relations can be obtained without relying on diagrammatic techniques.
• To determine if the new method can accommodate an unrestricted number of conservation laws.

Main Methods:

• Utilized generating functions to derive recursion relations.
• Did not rely on diagrammatic techniques.
• Focused on systems of degenerate fermions.

Main Results:

• Successfully derived recursion relations using generating functions.
• The generating function approach does not require explicit two-body interactions.
• This method is independent of the number of conservation laws considered.

Conclusions:

• Generating functions provide a versatile alternative to diagrammatic techniques for fermion systems.
• The proposed method offers greater flexibility in incorporating conservation laws.
• This approach enhances the applicability of recursion relations in condensed matter physics and quantum field theory.