Field theory on kappa-spacetime
Marija Dimitrijevic, Larisa Jonke, Lutz Moeller, Efrossini Tsouchnika,, Julius Wess, Michael Wohlgenannt
TL;DR
This paper develops a formalism for constructing field theories on quantum-deformed spacetimes, specifically demonstrating it for kappa-deformed Poincare algebra and deriving the Klein-Gordon equation.
Contribution
It introduces a general method to formulate field theories on quantum spaces with deformed symmetries, using star-products and algebraic mappings.
Findings
Formalism for quantum spacetime field theory established
Klein-Gordon equation derived in the deformed setting
Demonstration on kappa-deformed Poincare algebra and quantum space
Abstract
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the kappa-deformed Poincare algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable star-product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.
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