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Sergey Paston
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Analysis of topological effects in QED-2 in the framework of functional
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S.Paston
"Analysis of topological effects in QED-2
in the framework of functional integral formalism"
Abstract:
The Euclidian form of two-dimensional quantum electrodynamics is
investigated in which the configurations of gauge field with an
arbitrary integer topological number are permitted. The vacuum
parameter $\te$ is introduced into the theory by adding the
topological term, being a total divergence, to the Lagrangian
density. With the help of transformations of the functional
integral generating the Green functions, we reformulate the
theory to a form in which only enough fastly decreasing
configurations of the gauge field (i.e. having zero topological
number) are permitted. But in the action a new term arises which
is not equal to the total divergence and depends on the parameter
$\te$. One can interpret this term as a presence of the external
electric field with the strength $\te e/2\pi$. This coincides
with the known interpretation of the $\te$ parameter by
S.~Coleman. In the proposed formulation of the theory the vacuum
parameter $\te$ enters into the action as usual parameter. This
simplifies the study of its influence on the theory. Two
different methods of transformations of the functional integral,
in coordinate and in momentum spaces, are compared.
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