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Non-commutative space-time of Doubly Special Relativity theories
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abstract
Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there is infinitely many DSR constructions of the energy-momentum sector, each of whose can be promoted to the $\kappa$-Poincar\'e quantum (Hopf) algebra. Then we use the co-product of this algebra and the known construction of $\kappa$-deformed phase space via Heisenberg double in order to derive the non-commutative space-time structure and description of the whole of the DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space-time of the DSR theory is unique and equivalent to the theory with non-commutative space-time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space-time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space-time, its intrinsic length parameter $\ell$ becomes observer-independent.
Forward citations
Cited by 5 Pith papers
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The $q$-extension of iterated integrals and nested sums in quantum field theory
The authors define q-extended versions of the iterated integrals and nested sums used in QFT, deriving closed forms for simple cases and algorithmic recipes for complex ones.
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The $\mu$-extension of iterated integrals and nested sums
The authors construct μ-extensions of iterated integrals and nested sums over multiple alphabets, showing that they map polynomially in μ into the original function space (except for square-root cases) while preservin...
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Complex scalar field in \kappa-Minkowski noncommutative spacetime
The canonical Noether charges for the κ-deformed complex scalar match the covariant phase space results, and the earlier C-breaking is traced to using the twisted-cyclic Lagrangian L_C1 instead of the manifestly symme...
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A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
For the cubic entropy correction S=πr_h²−αr_h³ arising from a Planck-scale modified dispersion relation, all physically allowed Schwarzschild-like branches have winding number w=−1, so no stable phase appears.
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\kappa-deformed spin-1/2 field
A kappa-deformed Dirac action is constructed whose Noether charges close the standard Poincaré algebra, while charge conjugation symmetry is broken and CPT can only be restored by deforming time reversal.
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