arXiv subjects
Publications and source records attributed to Tomas Sykora.
We calculate the equal-time commutator of two fermionic currents within the framework of the 1+1 dimensional fully quantized theory, describing the interaction of massive fermions with a massive vector boson. It is shown that the interaction does not change the result obtained within the theory of free fermions.
The two different approaches - Källen's and Brandt's methods - for the calculations of the Schwinger terms in the 1+1 dimensional Abelian and non-Abelian free current algebras are discussed. These methods are applied to calculation of the single and double commutators. The validity of the Jacobi identities is examined in 1+1 and 3+1 dimensions and in this way is given natural restriction on the regularization. It is shown that the Jacobi identity cannot be broken in 1+1 dimensions even using the regularization which fails in the 3+1 dimensional case. A connection between the Schwinger term and anomaly is shown in the simplest case of the Schwinger model.
We analyze the generalized point-splitting method and Jo's result for the commutator anomaly. We find that certain classes of general regularization kernels satisfying integral conditions provide a unique result, which, however differs from Faddeev's cohomological result.