Lorentz-breaking weighted measures as quantum field theory regulators

Abstract

In this work we develop a re-formulation of quantum field theory through the more general weighted measures that the definition of quantum fields allows, and that violate explicitly the Lorentz symmetry; this approach provides finite answers for the long-live problems of the traditional formulations of quantum field theories, namely, smooth distributions for the field commutators that are finite a short distances, finite vacuum expectation values for the energy (without invoking normal ordering of operators), and finite fluctuations for the field operators. We shall show that the present scheme will allow us to construct an infinite family of noncommutative field theories that are compared with other formulations. Our regularization scheme breaks down for a massless field, which will be considered in future explorations.

Keywords

• Noncommutative quantum field theories
• Ultraviolet divergences
• Finite vacuum expectation values
• Finite quantum field theory