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SUMMARY:Operator-based method for finding exact solutions of the propagato
r equation in the presence of a magnetic field
DTSTART;VALUE=DATE-TIME:20181022T124000Z
DTEND;VALUE=DATE-TIME:20181022T151000Z
DTSTAMP;VALUE=DATE-TIME:20200606T115151Z
UID:indico-contribution-1261@cern.ch
DESCRIPTION:Speakers: STANISLAV IABLOKOV (P.G. Demidov Yaroslavl State Uni
versity)\nElementary particle processes in the extreme astrophysical condi
tions\, such as strong magnetic fields\, require knowledge of the exact pr
opagators. There are known expressions for the propagators of scalar\, Dir
ac and massive vector fields in the presence of the constant magnetic fiel
d both in the coordinate and in the momentum spaces. In general they requi
re either following the tedious Fock-Schwinger procedure or first obtainin
g the exact solutions of the wave equation of interest followed by summati
on over the allowed quantum numbers. In this work we present a general met
hod of obtaining the exact analytical solutions of the propagator equation
based on the decomposition of the delta function into the sum of the Hami
ltonian-like operator eigenfunctions with the subsequent integration of th
e corresponding operator exponent in the proper time domain. Providing tha
t parts of the operator exponent commute\, it becomes possible to decouple
them from each other and apply each part separately to the delta function
decomposition series. This method not just allows to straightforwardly ob
tain the expression for the propagator in the momentum space as a sum over
the Landau levels\, but also helps to gain insights into the propagator's
anatomy\, revealing the origins of its constituent parts.\n\nhttps://indi
co.particle.mephi.ru/event/22/contributions/1261/
LOCATION:Hotel Intourist Kolomenskoye 4* Petrovskiy hall
URL:https://indico.particle.mephi.ru/event/22/contributions/1261/
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