Sergey Paston

Analysis of topological effects in QED-2 in the framework of functional

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 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. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^