# Hamiltonians for systems of N particles interacting through point interactions

@article{DellAntonio1994HamiltoniansFS, title={Hamiltonians for systems of N particles interacting through point interactions}, author={Gianfausto Dell'Antonio and Rodolfo Figari and Alessandro Teta}, journal={Annales De L Institut Henri Poincare-physique Theorique}, year={1994}, volume={60}, pages={253-290} }

En utilisant des techniques de renormalisation de formes quadratiques singulieres, on etudie des Hamiltoniens pour systemes de N particules avec interactions de portee nulle, en dimension deux. Si on utilise la meme methode en dimension trois, on obtient des formes quadratiques qui, pour N = 3, ont une borne inferieure seulement si l'on impose des conditions de symetrie, et qui, pour N assez grand, n'ont, en tout cas, pas de borne inferieure

## 95 Citations

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- Mathematics, Physics
- 2004

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## 20 References

### ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR

- Mathematics
- 1974

We investigate the discrete spectrum of the Schr?dinger operator H for a system of three particles. We assume that the operators h?, ? = 1,?2,?3, which describe the three subsystems of two particles…

### On the finiteness of the discrete spectrum of Hamiltonians for quantum systems of three one- or two-dimensional particles

- Mathematics
- 1992

The system of three particles (acting in K dimensions (K=1, 2)) without stable two-particle subsystems is studied. For short-range potentials Vij(rij), the finiteness of the discrete spectrum is…

### Annales de l'Institut Henri Poincaré

- MathematicsNature
- 1931

The first number of the Annales was noticed in Nature of Oct. 11, 1930 (p. 564). In the second number we have de Donder on Einstein's theory of gravitation, Pólya on some points in the theory of…

### Binding of three identical bosons in two dimensions

- Physics
- 1979

Qualitative features are discussed for the binding of three identical bosons interacting through pair potentials in two dimensions. Two special cases, known to yield pathologies in three dimensions,…

### THREE BODY PROBLEM FOR SHORT RANGE FORCES. I. SCATTERING OF LOW ENERGY NEUTRONS BY DEUTERONS

- Physics
- 1957

An exact solution is obtained for the three body problem in the limiting case of a vanishingly small radius of action of the forces. In this case, the Schrodinger equation for the system of three…

### The non-relativistic limit ofP(ϕ)2 quantum field theories: Two-particle phenomena

- Physics, Philosophy
- 1977

It is proved that for two-particle phenomena theP(ϕ)2 quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a δ function potential in the limitc→∞.

### Solvable models in quantum mechanics

- Education
- 1990

Name: Helge Holden, Born: September 28, 1956 in Oslo. Norwegian nationality Position: Professor of mathematics Address: Department of Mathematical Sciences, NTNU Norwegian University of Science and…

### Quadratic forms for singular perturbations of the Laplacian

- Mathematics
- 1990

Singular perturbations of -Δ in L 2 (R 3 ) supported by points, regular curves an regular surfaces are considered. Using a renormalization technique the corresponding quadratic forms are constructed…