Scattering on a nonrelativistic particle in strong-coupling theory

V. D. Kamenetskii

R. Kh. Gainutdinov

The possibility of constructing a nonrelativistic scattering theory without appealing to the Schroedinger formalism is investigated, the theory being based on the general physical principles of causality, superposition, and unitarity. It is proved that the proposed approach is more general than the nonrelativistic scattering theory based on the Schroedinger equation. The proposed approach is used for the construction of a model scattering theory for a system consisting of heavy nonrelativistic particles and a light relativistic particle.

D. Rogers, Mitchel D. Kovarik, Jurij W. Darewych

The many-particle binding energy in the model [Formula: see text] in 1 + 1 dimensions is obtained using simple nonrelativistic quantum mechanics. We determine an effective two-particle potential from approximate field-theoretical solutions of the two-particle bound state and use it to obtain the many-particle binding energy. The results agree reasonably well with numerical calculations of the three- and four-particle binding energy in the field theory for weak coupling, λ. We also use this nonrelativistic potential to calculate the two-particle scattering amplitude.

Fritz Gesztesy

M. Mijatović, Gjorgji Ivanovski, B. Veljanoski +1 more

Soke Yuen Yong, Dam Thanh Son

We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with pointlike interaction. We identify an alternative type of interaction which depends on the relative velocity between the particles. We compute the renormalization-group running of the coupling constants and find a fixed point and a fixed line. We show that the scattering amplitudes can be expressed in terms of three parameters. The result matches with a quantum-mechanical analysis and represents the most general pointlike interaction consistent with unitarity and time-reversal invariance.