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

Duration of interactions in quantum electrodynamics: basic concepts, temporal features of kinetic phenomena

Mark E. Perel’man

For temporal magnitudes describing, in details, processes of particles scattering for a long time at each necessity case a particular, ad hoc reception were used. However the desirability of general approach basing on concepts of quantum field theory and uniting two main problems, durations of delay at scattering and of formation of arisen states, seems evident. We show that the Ward-Takahashi identity allows the defining of general temporal function in the frame of QED, real part of which describes the duration of delay of scattered particle on scatterer and imaginary part describes the duration of formation ("dressing") of outgoing bare particle. The functions of same form can be revealed in the known QED descriptions of processes, i.e. they arise in the course of standard calculations, but are not entered artificially. These functions submit to the operator of duration determinable by the reciprocal analogue of the Schroedinger equation, operator of which is canonically conjugated with Hamiltonian. Definition of temporal functions leads to the developing of such kinetic theories: theory of optical dispersion (with the decision of certain known paradoxes), theory of multiphoton processes (definitions of their thresholds and saturations) and theory of phase transitions (determination of general correlation radii and the full system of critical indices). The determination of temporal functions demonstrates also the instanton-type nature of tunneling processes, makes clear sense of the adiabatic hypothesis of quantum theory and some renormalization schemes. In an application to the problem of charge nullification they lead to a restriction of allowable number of fermions of the theory.For temporal magnitudes describing, in details, processes of particles scattering for a long time at each necessity case a particular, ad hoc reception were used. However the desirability of general approach basing on concepts of quantum field theory and uniting two main problems, durations of delay at scattering and of formation of arisen states, seems evident. We show that the Ward-Takahashi identity allows the defining of general temporal function in the frame of QED, real part of which describes the duration of delay of scattered particle on scatterer and imaginary part describes the duration of formation ("dressing") of outgoing bare particle. The functions of same form can be revealed in the known QED descriptions of processes, i.e. they arise in the course of standard calculations, but are not entered artificially. These functions submit to the operator of duration determinable by the reciprocal analogue of the Schroedinger equation, operator of which is canonically conjugated with Hamiltonian. Definition of temporal functions leads to the developing of such kinetic theories: theory of optical dispersion (with the decision of certain known paradoxes), theory of multiphoton processes (definitions of their thresholds and saturations) and theory of phase transitions (determination of general correlation radii and the full system of critical indices). The determination of temporal functions demonstrates also the instanton-type nature of tunneling processes, makes clear sense of the adiabatic hypothesis of quantum theory and some renormalization schemes. In an application to the problem of charge nullification they lead to a restriction of allowable number of fermions of the theory.

arXiv:0903.1823Mar 10, 20090 citations

Time Delay of Quantum Scattering Processes

Philippe Martin

Springer eBooksJan 1, 198131 citations

Time delays and advances in classical and quantum systems

Evgeni E. Kolomeitsev, D N Voskresensky

This article reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics and classical electrodynamics. Then we quantify durations of various quantum mechanical processes. The duration of the quantum tunneling is studied, and an interpretation of the Hartmann paradox is suggested. Time delays and advances appearing in the three-dimensional scattering problem on a central potential are considered. We then discuss delays and advances appearing in quantum field theory and after that we focus on the issue of time delays and advancements in quantum kinetics. We discuss problems of the application of generalized kinetic equations in simulations of the system relaxation toward equilibrium and analyze the kinetic entropy flow. Possible measurements of time delays and advancements in experiments similar to the recent OPERA neutrino experiment are also discussed.This article reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics and classical electrodynamics. Then we quantify durations of various quantum mechanical processes. The duration of the quantum tunneling is studied, and an interpretation of the Hartmann paradox is suggested. Time delays and advances appearing in the three-dimensional scattering problem on a central potential are considered. We then discuss delays and advances appearing in quantum field theory and after that we focus on the issue of time delays and advancements in quantum kinetics. We discuss problems of the application of generalized kinetic equations in simulations of the system relaxation toward equilibrium and analyze the kinetic entropy flow. Possible measurements of time delays and advancements in experiments similar to the recent OPERA neutrino experiment are also discussed.

arXiv:1301.3361Journal of Physics G Nuclear and Particle PhysicsOct 11, 201321 citations

Potential Scattering. The Radial Schrödinger Equation

K. Chadan

Elsevier eBooksJan 1, 20022 citations

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.