Related papers: Derivations and Reflection Positivity on the Quant…

The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum…

We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…

Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…

We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in…

We classify and construct all irreducible positive energy representations of the loop group of a compact, connected and simple Lie group and show that they admit an intertwining action of Diff(S^{1}).

We develop a novel perspective on reflection positivity (RP) on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes…

We generalize the derivation of the Wallis formula for $\pi$ from a variational computation of the spectrum of the Hydrogen atom. We obtain infinite product formulas for certain combinations of gamma functions, which include irrational…

We show that if the Kobayashi--Royden metric of a complex manifold is continuous and positive at a given point and any non-zero tangent vector, then the "derivatives" of the higher order Lempert functions exist and equal the respective…

We prove some existence and uniqueness results and some qualitative properties for the solution of a system modelling the catalytic conversion in a cylinder. This model couples parabolic partial differential equations posed in a cylindrical…

The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an…

We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor.…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…

In this paper we present an explicit construction for the fundamental solution to the Dirac and Laplace operator on some non-orientable conformally flat manifolds. We first treat a class of projective cylinders and tori where we can study…

A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.

We prove a generalized version of the Quantum Ergodicity Theorem on smooth compact Riemannian manifolds without boundary. We apply it to prove some asymptotic properties on the distribution of typical eigenfunctions of the Laplacian in…

This paper presents the logic QRC$_1$, which is a strictly positive fragment of quantified modal logic. The intended reading of the diamond modality is that of consistency of a formal theory. Predicate symbols are interpreted as…

Let $C$ be a smooth projective irreducible curve defined over a finite field $\mathbb{F}_q$ and $K=\mathbb{F}_q(C)$. Let $A\subset K$ be the ring of functions regular outside a fixed place $\infty$ of $K$. Let…

Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…

The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this $c$-duality are…

We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.