# Propagation of singularities in many-body scattering in the presence of bound states

Journées équations aux dérivées partielles (1999)

- page 1-20
- ISSN: 0752-0360

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topVasy, András. "Propagation of singularities in many-body scattering in the presence of bound states." Journées équations aux dérivées partielles (1999): 1-20. <http://eudml.org/doc/93373>.

@article{Vasy1999,

abstract = {In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u\in \mathcal \{S\}^\{\prime \}$ of $(H-\lambda )u=0$, where $H$ is a many-body hamiltonian $H=\Delta +V$, $\Delta \ge 0$, $V=\sum _a V_a$, and $\lambda $ is not a threshold of $H$, under the assumption that the inter-particle (e.g. two-body) interactions $V_a$ are real-valued polyhomogeneous symbols of order $-1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the set of singularities of $u$ is a union of maximally extended broken bicharacteristics of $H$. These are curves in the characteristic variety of $H$, which can be quite complicated due to the existence of bound states. We use this result to describe the wave front relation of the S-matrices. Here we only present the statement of the results and sketch some of the ideas in proving them, the complete details will appear elsewhere.},

author = {Vasy, András},

journal = {Journées équations aux dérivées partielles},

keywords = {wave front relation of the S-matrices},

language = {eng},

pages = {1-20},

publisher = {Université de Nantes},

title = {Propagation of singularities in many-body scattering in the presence of bound states},

url = {http://eudml.org/doc/93373},

year = {1999},

}

TY - JOUR

AU - Vasy, András

TI - Propagation of singularities in many-body scattering in the presence of bound states

JO - Journées équations aux dérivées partielles

PY - 1999

PB - Université de Nantes

SP - 1

EP - 20

AB - In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u\in \mathcal {S}^{\prime }$ of $(H-\lambda )u=0$, where $H$ is a many-body hamiltonian $H=\Delta +V$, $\Delta \ge 0$, $V=\sum _a V_a$, and $\lambda $ is not a threshold of $H$, under the assumption that the inter-particle (e.g. two-body) interactions $V_a$ are real-valued polyhomogeneous symbols of order $-1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the set of singularities of $u$ is a union of maximally extended broken bicharacteristics of $H$. These are curves in the characteristic variety of $H$, which can be quite complicated due to the existence of bound states. We use this result to describe the wave front relation of the S-matrices. Here we only present the statement of the results and sketch some of the ideas in proving them, the complete details will appear elsewhere.

LA - eng

KW - wave front relation of the S-matrices

UR - http://eudml.org/doc/93373

ER -

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