Physical Review

Concerning the Notion of "Time Interval" in S -Matrix Theory

M. L. Goldberger, Kenneth Watson

Published Sep 15, 1962• 41 citations

Abstract

The notion of time duration is considered within the framework of $S$-matrix theory. It is shown that Wigner's definition of the time delay, $\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]$, for a scattering process permits one to define time duration in a "coarse-grained" sense.

DOI: 10.1103/physrev.127.2284

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Physical Review

Concerning the Notion of "Time Interval" in S -Matrix Theory

M. L. Goldberger, Kenneth Watson

Published Sep 15, 1962• 41 citations

Publisher

Abstract

The notion of time duration is considered within the framework of

S

-matrix theory. It is shown that Wigner's definition of the time delay,

\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]

, for a scattering process permits one to define time duration in a "coarse-grained" sense.

DOI: 10.1103/physrev.127.2284

Related papers

Reciprocal Schrödinger Equation: Durations of Delay and of Final States Formation in Processes of Scattering

Mark E. Perel’man

The reciprocal Schrödinger equation $\partial S(ω,{\bf r}% )/i\partial ω=\hatτ(ω,{\bf r}) S(ω,{\bf r})$ for $S$ -matrix with temporal operator instead the Hamiltonian is established via the Legendre transformation of classical action function. Corresponding temporal functions are expressed via propagators of interacting fields. Their real parts $τ_{1}$ are equivalent to the Wigner-Smith delay durations at process of scattering and imaginary parts $τ_{2}$ express the duration of final states formation (dressing). As an apparent example, they can be clearly interpreted in the oscillator model via polarization ( $% τ_{1}$ ) and conductivity ( $τ_{2}$ ) of medium. The $τ$ -functions are interconnected by the dispersion relations of Kramers-Krönig type. From them follows, in particular, that $τ_{2}$ is twice bigger than the uncertainty value and thereby is measurable; it must be negative at some tunnel transitions and thus can explain the observed superluminal transfer of excitations at near field intervals (M.E.Perel'man. In: arXiv. physics/0309123). The covariant generalizations of reciprocal equation clarifies the adiabatic hypothesis of scattering theory as the requirement: $% τ_{2}\to 0$ at infinity future and elucidate the physical sense of some renormalization procedures.The reciprocal Schrödinger equation $\partial S(ω,{\bf r}% )/i\partial ω=\hatτ(ω,{\bf r}) S(ω,{\bf r})$ for $S$-matrix with temporal operator instead the Hamiltonian is established via the Legendre transformation of classical action function. Corresponding temporal functions are expressed via propagators of interacting fields. Their real parts $τ_{1}$are equivalent to the Wigner-Smith delay durations at process of scattering and imaginary parts $τ_{2}$ express the duration of final states formation (dressing). As an apparent example, they can be clearly interpreted in the oscillator model via polarization ($% τ_{1}$) and conductivity ($τ_{2}$) of medium. The $τ$-functions are interconnected by the dispersion relations of Kramers-Krönig type. From them follows, in particular, that $τ_{2}$ is twice bigger than the uncertainty value and thereby is measurable; it must be negative at some tunnel transitions and thus can explain the observed superluminal transfer of excitations at near field intervals (M.E.Perel'man. In: arXiv. physics/0309123). The covariant generalizations of reciprocal equation clarifies the adiabatic hypothesis of scattering theory as the requirement: $% τ_{2}\to 0$ at infinity future and elucidate the physical sense of some renormalization procedures.

arXiv:quant-ph/0311169Nov 25, 20030 citations

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Hanns Georg Kilian

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Serge Richard

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Serge Richard, Rafael Tiedra de Aldecoa

arXiv:1008.3433Aug 20, 20101 citation

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Massimiliano Sassoli de Bianchi

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Jan 1, 201212 citations

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Massimiliano Sassoli de Bianchi

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arXiv:1010.5329Open PhysicsDec 12, 201112 citations

The notion of time duration is considered within the framework of

S

-matrix theory. It is shown that Wigner's definition of the time delay,

\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]

, for a scattering process permits one to define time duration in a "coarse-grained" sense.

The reciprocal Schrödinger equation

\partial S(ω,{\bf r}% )/i\partial ω=\hatτ(ω,{\bf r}) S(ω,{\bf r})

for

S

-matrix with temporal operator instead the Hamiltonian is established via the Legendre transformation of classical action function. Corresponding temporal functions are expressed via propagators of interacting fields. Their real parts

τ_{1}

are equivalent to the Wigner-Smith delay durations at process of scattering and imaginary parts

τ_{2}

express the duration of final states formation (dressing). As an apparent example, they can be clearly interpreted in the oscillator model via polarization (

% τ_{1}

) and conductivity (

τ_{2}

) of medium. The

τ

-functions are interconnected by the dispersion relations of Kramers-Krönig type. From them follows, in particular, that

τ_{2}

is twice bigger than the uncertainty value and thereby is measurable; it must be negative at some tunnel transitions and thus can explain the observed superluminal transfer of excitations at near field intervals (M.E.Perel'man. In: arXiv. physics/0309123). The covariant generalizations of reciprocal equation clarifies the adiabatic hypothesis of scattering theory as the requirement:

% τ_{2}\to 0

at infinity future and elucidate the physical sense of some renormalization procedures.