Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reciprocal Schr\"{o}dinger Equation: Durations of Delay and of Final
  States Formation in Processes of Scattering   The reciprocal Schr\"{o}dinger equation $\partial S(\omega ,{\bf r}%
)/i\partial \omega =\hat{\tau}(\omega ,{\bf r}) S(\omega ,{\bf r})$ 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 $\tau_{1}$are equivalent to the Wigner-Smith delay durations at
process of scattering and imaginary parts $\tau_{2}$ express the duration of
final states formation (dressing). As an apparent example, they can be clearly
interpreted in the oscillator model via polarization ($% \tau_{1}$) and
conductivity ($\tau_{2}$) of medium. The $\tau $-functions are interconnected
by the dispersion relations of Kramers-Kr\"{o}nig type. From them follows, in
particular, that $\tau_{2}$ 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: $% \tau_{2}\to 0$ at infinity future and
elucidate the physical sense of some renormalization procedures.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys