We show that under generic conditions, the quantisation of a $1$-parameter family KAM perturbations $P(x,\xi;t)$ completely integrable and Kolmogorov non-degenerate Gevrey smooth Hamiltonian is not quantum ergodic, at least for full measure subset parameter $t\in (0,\delta)$.

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

It is argued that the quantum of area between consecutive, high overtones quasinormal modes a black hole horizon coincides with gap predicted by Loop Quantum Gravity, as long isolated and Barbero-Immirzi parameter $\gamma \approx \sqrt{3}/6$, in agreement value derived from Bekenstein-Hawking entropy.

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP3, compactified Minkowski space CM and the twistor correspondence space are obtained along with their canonical quantum differential...

For over six decades, quantum electrodynamics (QED) in multipolar form has been an invaluable tool for understanding quantum-scale atomic and molecular interactions. However, its relation to the Poincare-gauge a recent topic of controversy debate. It was claimed by Rousseau Felbacq article Scientific Reports 7, 11115 (2017) that Hamiltonian QED is not same as it generally equivalent Coulomb-gau...

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate string theory in T-fold backgrounds with T-duality transition functions and a quantum implementation of the constraints of the doubled formalism is presented....

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

We prove that the skein categories of Walker–Johnson-Freyd satisfy excision. This allows us to conclude are k-linear factorisation homology and taking free cocompletion recovers locally finitely presentable homology. An application this is algebra a punctured surface related any quantum group with generic parameter gives quantisation associated character variety.

In a recent proposal we applied methods from constructive QFT to derive Hamiltonian Renormalisation Group in order employ it ultimately for canonical quantum gravity. The was successfully tested free scalar fields and thus natural next step is test gauge theories. This can be done the framework of reduced phase space quantisation which allows using techniques developed earlier field addition, g...