The quantum N-body problem and the auxiliary field method
Bernard Silvestre-Brac, Claude Semay, Fabien Buisseret, Fabian Brau
TL;DR
This paper develops approximate analytical energy formulas for N-body relativistic Hamiltonians using the auxiliary field method, demonstrating its effectiveness in atomic and hadronic physics, including baryon systems.
Contribution
It extends the auxiliary field method to N-body relativistic systems, providing a general procedure and applying it to atomic and hadronic Hamiltonians.
Findings
Derived analytical energy formulas for N-body systems
Validated formulas with baryon three-quark system test
Demonstrated method's applicability in atomic and hadronic physics
Abstract
Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.
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