Relativistic three-body problem in three-dimensional variables

Three-body problem at finite temperature and density

“…We base our derivation of the in-matter three-body equation on that of Ref. [14]. By contrast, other recent many-body formulations of three-body equations have been closely related to the work of Ref.…”

“…From the very beginning, it was recognized that Faddeev's approach [12] provided a powerful tool in the description of few-body properties in Quantum Mechanics. It is therefore natural that not long after its formulation, this approach was also applied to quantum field theory, first within a four-dimensional formulation [13], and then within a three-dimensional one obtained by equating times in four-dimensional Green functions [14]. These early formulations were for three particles in vacuum.…”

Bound state equation for 4 or more relativistic particles

“…Special cases of N=2 or 3-fermion systems were examined. Taking the retarded part of the full propagator at equal times, following Logunov and Tavkhelidze [4] (for two particles) and Kvinikhidze and Stoyanov [21] (for three particles) also leads to the same 3D equations.…”

“…The integrations with respect to the relative energies preserve the positions of the bound state poles of G (it can also be shown that the physical particleparticle, particle-bound state or bound state-bound state scattering amplitudes are also preserved [21,20]). If we write G as…”

“…This 3D full propagator is, in configuration space, the retarded part of G taken at equal times. It has been the starting point of a 3D reduction by Logunov and Tavkhelidze [4] (in the two-fermion case), followed by Kvinikhidze and Stoyanov [21] (three fermions) and Khvedelidze and Kvinikhidze [25] (four fermions).…”