Abstract
In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After a review of the κ-Poincaré algebra, we illustrate the construction of the κ-deformed phase space of a classical relativistic particle using the tools of Lie bi-algebras and Poisson–Lie groups. We then discuss how to construct a free scalar field theory on the non-commutative κ-Minkowski space associated to the κ-Poincaré and illustrate how the group valued nature of momenta affects the field propagation.
Highlights
Introduction to κDeformedSymmetries, Phase Spaces andField Theory
Quantum group deformations of relativistic spacetime symmetries became a popular topic in the quantum gravity research community in the early 2000s mainly thanks to the development of the ideas of doubly special relativity (DSR), proposed by Amelino-Camelia in two papers [1,2]
If Lorentz symmetry is to hold, how is it possible that this length scale does not depend on the observer measuring it? As an example, let us consider one of the major results of loop quantum gravity: the discreteness of the spectrum of area and volume operators, with their spectra bounded from below, by, roughly, `2 and3, whereis the Planck length
Summary
Quantum group deformations of relativistic spacetime symmetries became a popular topic in the quantum gravity research community in the early 2000s mainly thanks to the development of the ideas of doubly special relativity (DSR), proposed by Amelino-Camelia in two papers [1,2]. These papers pose the question of whether it is possible to reconcile. We conclude this review with a brief outlook of the open challenges in the field
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