The connection between causality and analyticity in scattering theory is formulated in terms of Hilbertspace concepts. The usual rules of nonrelativistic quantum mechanics are assumed to hold for the "in" and "out" states of the scattering system. We show that there is a (physically verifiable) causality condition which implies that each diagonal $S$ -matrix element ${S}_{\ensuremath{\alpha}\ensuremath{\alpha}}(E)$ must be the limit of an analytic function of the energy $E$ , regular in $\mathrm{Im}E>0$ . The implications for partial-wave amplitudes and for the forward scattering amplitude in elastic two-body collisions are discussed.The connection between causality and analyticity in scattering theory is formulated in terms of Hilbertspace concepts. The usual rules of nonrelativistic quantum mechanics are assumed to hold for the "in" and "out" states of the scattering system. We show that there is a (physically verifiable) causality condition which implies that each diagonal $S$-matrix element ${S}_{\ensuremath{\alpha}\ensuremath{\alpha}}(E)$ must be the limit of an analytic function of the energy $E$, regular in $\mathrm{Im}E>0$. The implications for partial-wave amplitudes and for the forward scattering amplitude in elastic two-body collisions are discussed.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 19716 citations

Microcosmic study of digital human body: scattering theory model of quantum human body

BI Si-wen

Scattering theoretical model is the main content of the study of quantum human body information mechanism. The interaction idea of quantum human body, the functor of quantum human body state evolving with time and the outspread of tiny disturbing theory of quantum human body were discussed in this paper. The scattering matrix of quantum human body, the outspread of tiny disturbing theory of quantum human body S matrix, the scattering section of quantum human body and the disparting wave method of quantum human body were expounded. Finally, the author summarized from seven aspects to the whole paper. Theoretical models were provided for the study of scattering mechanism of quantum human body.Scattering theoretical model is the main content of the study of quantum human body information mechanism. The interaction idea of quantum human body, the functor of quantum human body state evolving with time and the outspread of tiny disturbing theory of quantum human body were discussed in this paper. The scattering matrix of quantum human body, the outspread of tiny disturbing theory of quantum human body S matrix, the scattering section of quantum human body and the disparting wave method of quantum human body were expounded. Finally, the author summarized from seven aspects to the whole paper. Theoretical models were provided for the study of scattering mechanism of quantum human body.

Zhongguo yixue yingxiang jishuJan 1, 20050 citations

Some results on many-body scattering theory

Paul G. Federbush

Annals of PhysicsSep 1, 19682 citations

Renormalized Perturbation Expansion in Kinetic Theory

Ralf Der

Abstract Ladder summation techniques are applied to the recently developed c‐number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T‐matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell‐Boltzmann statistics), the T‐matrix introduced coincides with the usual T‐matrix of conventional two‐body scattering theory in free space. In low‐temperature Fermi systems, the T‐matrix differs from the reaction matrix of the Brueckner‐Goldstone theory because the “healing” property of the two‐body wave function does not obtain.Abstract Ladder summation techniques are applied to the recently developed c‐number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T‐matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell‐Boltzmann statistics), the T‐matrix introduced coincides with the usual T‐matrix of conventional two‐body scattering theory in free space. In low‐temperature Fermi systems, the T‐matrix differs from the reaction matrix of the Brueckner‐Goldstone theory because the “healing” property of the two‐body wave function does not obtain.

Annalen der PhysikJan 1, 19776 citations

S

-matrix element ${S}_{\ensuremath{\alpha}\ensuremath{\alpha}}(E)$ must be the limit of an analytic function of the energy

E

, regular in

\mathrm{Im}E>0

. The implications for partial-wave amplitudes and for the forward scattering amplitude in elastic two-body collisions are discussed.