Braided Field Quantization from Quantum Poincare Covariance

Abstract

We demonstrate that the covariance of the algebra of quantum NC fields under quantum-deformed Poincare symmetries implies the appearence of braided algebra of fields and the notion of braided locality in NC QFT. We briefly recall the historical development of NC QFT which was firstly formulated in the framework using classical relativistic symmetries but further it was described as generated by the quantum-deformed symmetries. We argue that consistent covariant quantum-deformed formalism requires "braiding all the way", in particular braided commutator of deformed field oscillators as well as the braid between the field oscillators and noncommutative Fourier exponentials. As example of braided quantum-deformed NC QFT we describe the NC scalar free fields on noncommutative canonical (Moyal-Weyl) space-time with braided c-number field commutator which implies braided locality.

14 pages; based on a talk presented at the meeting devoted to the Scientific and Human Legacy of Julius Wess, Serbia, August 2011, published also in electronic form in IJMP Conf. Series vol. 13 (2012) 127-140

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Cited by in corpus (3)

• Unified description for kappa-deformations of orthogonal groups
• Kappa-Deformations: Historical Developments and Recent Results
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries