Toward the classification of differential calculi on κ-Minkowski space and related field theories

Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina (2015) Toward the classification of differential calculi on κ-Minkowski space and related field theories. Journal of High Energy Physics (7). 055-1-055-33. ISSN 1029-8479

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Abstract

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincar\'e Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

Item Type:

Article

Uncontrolled Keywords:

non-commutative geometry; quantum groups; differential and algebraic geometry; space-time symmetries

Subjects:

NATURAL SCIENCES > Physics

Divisions:

Theoretical Physics Division

Projects: