93 citations · 134 across the 18 of their papers we have counts for
19 papers
Geometric Aharonov-Bohm phase effect around a black hole
Kaushlendra Kumar, Shahn Majid
In recent work, we have explored the novel possibility that the geodesic of a spacetime density flow in GR could be upgraded to an amplitude with density . We now show h…
Time-slicing quantum spacetimes
Shahn Majid
For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value of a coordinate time, with corresponding me…
Algebraic approach to quantum gravity IV: applications
Shahn Majid
We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calcula…
Geodesic flows on a black-hole background
Kaushlendra Kumar, Shahn Majid
A recent notion of geodesic flows which comes out of noncommutative geometry but which is also novel in the classical case is studied in detail for a Schwarzschild spacetime. In th…
Quantum variational calculus on a lattice
Shahn Majid, Francisco Simão
We solve the long-standing problem of variational calculus on a noncommutative space or spacetime for a significant class of models with trivial jet bundle. Our approach entails a…
Kaluza-Klein ansatz from Lorentzian quantum gravity on the fuzzy sphere
Chengcheng Liu, Shahn Majid
If Kaluza-Klein ideas were correct as an explanation of Yang-Mills and General Relativity on spacetime, the extra fibre geometry would have to be a sphere of constant size of the o…
Quantum jet Hopf algebroids by cotwist
Xiao Han, Shahn Majid
We introduce a cotwist construction for Hopf algebroids that also entails cotwisting or `quantisation' of the base and which is dual to a previous twisting construction of P. Xu. W…
Klein-Gordon flow on FLRW spacetimes
Edwin Beggs, Shahn Majid
We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of…
*-Hopf algebroids
Edwin Beggs, Xiao Han, Shahn Majid
We introduce a theory of -structures for bialgebroids and Hopf algebroids over a -algebra, defined in such a way that the relevant category of (co)modules is a bar category.…
Generally covariant quantum mechanics
Edwin Beggs, Shahn Majid
We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold as part of the construction of quantum geodesics on the algebra of diffe…
Complex structure on quantum-braided planes
Edwin Beggs, Shahn Majid
We construct a quantum Dolbeault double complex on the quantum plane . This solves the long-standing problem that the standard differential calcul…
Quantum geometric Wigner construction for and braided racks
Shahn Majid, Leo Sean McCormack
The quantum double of a finite group plays an important role in the Kitaev model for quantum computing, as well as in associated TQFT's, as a kind…
Curvature fluctuations in a baby quantum gravity model
Samuel Blitz, Shahn Majid
Understanding the microscopic behavior of spacetime is critical for developing a theory of quantum gravity and perhaps solving the cosmological constant problem. In this context, i…
Quantum Gravity: are we there yet?
Shahn Majid
The turn of the millennium was a time of optimism about an approach to noncommutative geometry inspired by rich mathematical objects called `quantum groups' and its applications to…
Quantization by cochain twists and nonassociative differentials
E. J. Beggs, S. Majid
We show that several standard associative quantizations in mathematical physics can be expressed as cochain module-algebra twists in the spirit of Moyal products at least to $O(\hb…
Quantum Groups and Noncommutative Geometry
S. Majid
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on th…
Quasitriangular and differential structures on bicrossproduct Hopf algebras
E. Beggs, S. Majid
Let X=GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra $H=kM\cobicross k(G)$ is itself a bicrossproduct $k…
Quantum Geometry and the Planck Scale
S. Majid
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation…
Finite Group Factorisations and Braiding
E. Beggs, J. Gould, S. Majid
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra associated to the factorization of a finite group int…