Annales Henri Poincaré

, Volume 20, Issue 11, pp 3509–3541 | Cite as

A Nonrelativistic Quantum Field Theory with Point Interactions in Three Dimensions

  • Jonas LampartEmail author


We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction between the two types of particles is a point interaction concentrated on the points in configuration space where the positions of two different particles coincide. We define the operator, and its domain of self-adjointness, in terms of co-dimension-three boundary conditions on the set of collision configurations relating sectors with different numbers of particles.



I am grateful to Stefan Keppeler, Julian Schmidt, Stefan Teufel and Roderich Tumulka for many interesting discussions on the subject of interior-boundary conditions.


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Authors and Affiliations

  1. 1.CNRS & Laboratoire interdisciplinaire Carnot de Bourgogne (UMR 6303)Université de Bourgogne Franche-ComtéDijon CedexFrance

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