# The quantum N-body problem and the auxiliary field method

## 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.

## Key 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.