Related papers: Observables as functions: Antonymous functions
Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
The extension of FRT quantization theory for the nonsemisimple CK groups is suggested. The quantum orthogonal CK groups are realized as the Hopf algebras of the noncommutative functions over an associative algebras with nilpotent…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
For functions defined on C^n or (R_+)^n we construct a dequantization transform, which is closely related to the Maslov dequantization. The subdifferential at the origin of a dequantized polynomial coincides with its Newton polytope. For…
It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…
We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the shape of the diagram. We prove that the algebra of such…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and…
We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral…
The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The…
Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…
This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This…
We discuss some basic properties of the Sibony functions and pseudometrics.
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
We view the neat reduct operator as a functor that lessens dimensions from CA_{\alpha+\omega} to CA_{\alpha} for infinite ordinals \alpha. We show that this functor has no right adjoint. Conversely for polyadic algebras, and several reducts…