The quantum N-body problem and the auxiliary field method

Abstract

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one-and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proven 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.

The Quantum N-Body Problem and the Auxiliary Field Method: New Developments

“…The method can also be extended to semirelativistic Hamiltonians [8] and to N -body systems [9]. In this last case, it is specially powerful for identical particles.…”

“…Formula (12) looks like a semiclassical approximation but this absolutely not the case. The AFM yields approximate N -body wavefunctions [9], and the relation (13) between p 0 and r 0 is a full quantum link, function of the quantum numbers of the system. At last, the value of r 0 (and thus of p 0 ) is the solution of a transcendental equation (14) which is the translation into the AFM variables of the generalized virial theorem [13].…”

Static properties of light baryons in different large-N limits

“…where ∑ M i=1 p p p i = 0 0 0 and R R R is the center of mass coordinate [16]. U(x) is a one-body potential and V (x) is a two-body potential.…”

“…It can then be shown that the AFM solution of the Hamiltonian (2.1) is obtained by solving the following set of equations [16,17,18,19] …”

“…We have analytically proved that the static properties of light baryons scale as expected [14,15]. All approximate solutions for the many-body Hamiltonians considered have been obtained using the auxiliary field method (AFM) [16,17,18,19].…”