7 papers
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…