It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class quantum models in which these plus the underlying physical Hilbert-space metric $\Theta$ are all represented terms auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\ldots,N$. Our formalism degenerates to ${\...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

Leading order study of direct photon production from proton–proton collisions, in the framework Minimal (Seiberg–Witten) Non-Commutative Standard Model (NCSM), taking into account Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high transverse momentum. Therefore, using Run-1 ([Formula: see text] TeV) and Run-2 ATLAS experimental data ...

We present a self-contained and comprehensive study of the Fisher-Rao space matrix-valued non-commutative probability measures, related Hellinger space. Our is natural generalization classical commutative measures Bures-Wasserstein Hermitian positive-definite matrices. introduce justify canonical entropy on space, which differs from von Neumann entropy. consequently derive analogues heat flow, ...