scholarly journals Spectral and scattering theory for differential and Hankel operators

2017 ◽  
Vol 308 ◽  
pp. 713-766
Author(s):  
D.R. Yafaev
Keyword(s):  
Scattering Theory ◽  
Hankel Operators ◽  
Spectral And Scattering Theory

ASYMPTOTIC COMPLETENESS IN QUANTUM IN FIELD THEORY: MASSIVE PAULI–FIERZ HAMILTONIANS

1999 ◽  
Vol 11 (04) ◽  
pp. 383-450 ◽  
Author(s):  
J. DEREZIŃSKI ◽  
C. GÉRARD
Keyword(s):  
Field Theory ◽  
Scattering Theory ◽  
Geometric Analysis ◽  
Asymptotic Completeness ◽  
Spectral And Scattering Theory ◽  
Asymptotic Fields

Spectral and scattering theory of massive Pauli–Fierz Hamiltonians is studied. Asymptotic completeness of these Hamiltonians is shown. The proof consists of three parts. The first is a construction of asymptotic fields and a proof of their Fock property. The second part is a geometric analysis of observables. Its main result is what we call geometric asymptotic completeness. Finally, the last part is a proof of asymptotic completeness itself.

ON SPECTRAL AND SCATTERING THEORY FOR N-BODY, SCHRÖDINGER OPERATORS IN A CONSTANT MAGNETIC FIELD

2002 ◽  
Vol 14 (02) ◽  
pp. 199-240 ◽  
Author(s):  
TADAYOSHI ADACHI
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Scattering Theory ◽  
Short Range ◽  
Asymptotic Completeness ◽  
The Other ◽  
Conjugate Operator ◽  
Neutral Particles ◽  
Pair Potentials ◽  
Spectral And Scattering Theory

We consider an N-body quantum system in a constant magnetic field which consists of just one charged and the other N - 1 neutral particles. We prove the existence of a conjugate operator for the Hamiltonian which governs the system, and show the asymptotic completeness of the system under short-range assumptions on the pair potentials.

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