Abstract:
Starting from the second quantizied functional integral representation for field path-integral representation for the total many-particle Green function for relativistic and nonrelativistic point-like charged Bose and Fermi particles in $(3+1)$ or in $(2+1)$ interacting via Maxwell or Chern-Simon fields is constructed and shown to be only an integral over the trajectories of the particles. The effective action depends on coordinates and velocities of the particles, and is nonlocal in time due to causal interactions between the particles. In static (nonrelativistic) approximation the action is local in time and leads to expressions for the Hamiltonian for Coulomb interaction in $(3+1)$, and for anyon interaction in $(2+1)$ dimensions. This path integral representation automatically includes the usual connection between spin and statistics for the cases of infinite flat space and trivial topology for the manifold of the charged fields. Our results are generalized in the presence of an external magnetic field. It is shown how to take into account the contribution of the vacuum polarization effects in the framework of the approach.
Citation:
V. Ya. Fainberg, N. K. Pak, “A new path-integral representation for the many-particle Green function of the relativistic particles”, TMF, 103:2 (1995), 328–338; Theoret. and Math. Phys., 103:2 (1995), 595–602
\Bibitem{FaiPak95}
\by V.~Ya.~Fainberg, N.~K.~Pak
\paper A~new path-integral representation for the many-particle Green function of the relativistic particles
\jour TMF
\yr 1995
\vol 103
\issue 2
\pages 328--338
\mathnet{http://mi.mathnet.ru/tmf1307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1470951}
\zmath{https://zbmath.org/?q=an:0962.81525}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 103
\issue 2
\pages 595--602
\crossref{https://doi.org/10.1007/BF02274038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TD56100013}
Linking options:
https://www.mathnet.ru/eng/tmf1307
https://www.mathnet.ru/eng/tmf/v103/i2/p328
This publication is cited in the following 2 articles:
C. Tian, “Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture”, Annalen der Physik, 522:1-2 (2010), 75
Y. Itin, Yu.N. Obukhov, F.W. Hehl, “An electric charge has no screw sense – a comment on the twistfree formulation of electrodynamics by da Rocha and Rodrigues”, Annalen der Physik, 522:1-2 (2010), 35
Citation in format AMSBIB
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