On the Invariant Regularization in Relativistic Quantum Theory

Non invariant zeta - function regularization in quantum Liouville theory 1

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace-Beltrami operator covariant under conformal transformations, the other to the naive non invariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regular...

A New Gauge-Invariant Regularization Scheme Based on Lorentz-Invariant Noncommutative Quantum Field Theory

The IR/UV mixing in the non-commutative (NC) field theory is investigated in CarlsonCarone-Zobin (CCZ) formalism of Lorentz-invariant NC field theory provided that the fields are ‘independent’ of the ‘internal’ coordinates θ . A new regularization scheme called NC regularization is then proposed, which removes the Lorentz-invariant IR singularity by subtraction from the theory. It requires the ...

Relativistic Quantum Field Theory

On strategy of relativistic quantum theory construction

Two different strategies of the relativistic quantum theory construction are considered and evaluated. The first strategy is the conventional strategy, based on application of the quantum mechanics technique to relativistic systems. This approach cannot solve the problem of pair production. The apparent success of QFT at solution of this problem is conditioned by the inconsistency of QFT, when ...

Invariant Regularization of Supersymmetric Chiral Gauge Theory

We formulate a manifestly supersymmetric gauge covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has a covariant form and can emerge only in one-loop diagrams with all the external lines being the background gauge superfield...