C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

Více o knize

The relevance of commutator methods in spectral and scattering theory has long been recognized, yielding numerous notable results. For further insight, readers can refer to works by Putnam, Reed-Simon, and Baumgartel-Wollenberg. A significant advancement occurred around 1979 with E. Mourre's introduction of locally conjugate operators, which greatly enhanced the understanding of spectral properties in N-body Hamiltonians. This method simplified the previously challenging problem of proving the absence of singularly continuous spectrum for such operators, a feat accomplished by Mourre for N = 3 and later by Perry, Sigal, and Simon for general N. The Mourre estimate, central to this approach, also impacts the long-term behavior of N-body systems. In 1985, Sigal and Soffer further explored these propagation properties, establishing the existence and completeness of wave operators for N-body systems with short-range interactions, without imposing implicit conditions on the potentials. Prior to this, similar results for N = 3 were achieved through time-dependent methods by Enss and Sinha, Krishna, and Muthuramalingam. Our interest in commutator methods stems from these significant advancements.