arXiv subjects
Gavriel Segre
Publications and source records attributed to Gavriel Segre.
Magnetic Bottles on Riemann Surfaces
Yves Colin de Verdiere's quantization formalism of magnetic bottles on Riemann surfaces of non null genus is shown to be affected, owing to the Homotopy Superselection Rule, by the phenomenon of the existence of multiple inequivalent quantizations mathematically analogous to the phenomenon of the existence of multiple inequivalent prequantizations of a multiply-connected symplectic manifold in the framework of Souriau-Kostant's Geometric Quantization.
Classification of the automorphisms of the noncommutative torus among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones
Adopting the measure of quantum complexity, the quantum logical depth, previously introduced by the author the automorphisms of the noncommutative torus are classified among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones.
Quantum Democracy Is Possible
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't extend to the quantum case.
The natural definition of the quantum dynamical entropy in the framework of deformation quantization
It is shown how, in the framework of deformation quantization, the quantum dynamical entropy may be simply defined as the Kolmogorov-Sinai's entropy of the quantum flow.
An interesting temporalization of Gödel's ontological proof
Recent theologies concerning God's death after Auschwitz are mathematically formalized through a suitable temporalization of Gödel's Ontological Proof.
Martin Löf - Solovay - Chaitin Axiom of Reduction versus Von Mises - Church Axiom of Reduction
Under the assumption that the quantum random number generator Quantis by Id Quantique is a fair quantum coin, experimental indications of the fact that independent tosses of a quantum coin don't pass the Iterated Logarithm Randomness' Test are shown. The consequential observed experimental violation of the Martin Löf - Solovay - Chaitin Axiom of Reduction of Quantum Mechanics is then interpreted as the indication of the necessity of replacing it with the weaker Von Mises - Church Axiom of Reduction whose Game Theoretic meaning is explained.
Quantum substitutions of Pisot type, their quantum topological entropy and their use for optimal spacing
Quantum substitutions of Pisot type (and their quantum topological entropy) are introduced. Their utility as algorithms for optimal spacing is analyzed.
Phase operator of the quantum supersymmetric harmonic oscillator
After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic oscillators, the phase operator of the quantum fermionic harmonic oscillator and of the quantum supersymmetric harmonic oscillator are introduced and their properties analyzed. It is then shown that the phase operator of a supersymmetric harmonic oscillator is a Goldstone operator at any strictly positive temperature (finite or infinite).
Time-reversal properties in the coupling of quantum angular momenta
After a synoptic panorama about some still unsolved foundational problems involving time-reversal, we show that the \emph{double time-reversal superselection rule} of Nonrelativistic Quantum Mechanics is redundant. We then analyze which, among the symmetries of the Clebsch-Gordan coefficients, may be inferred through time-reversal considerations. Finally, we show how Coupling Theory allows to improve our comprehension of the fact that, in presence of hidden symmetries, Wigner's Theorem concerning Kramers degeneration cannot be applied, by analyzing a set of Z uncoupled massive particles, both in the case in which they are bosons of spin zero and in the case in which they are fermions of spin 1/2, subjected to a Keplerian force's field and considering the coupling of the 2Z quantum angular momenta resulting by the hidden SO(4) symmetry owed to the fact that, apart from the rotational SO(3) symmetry responsible of the conservation of the angular momentum, the Laplace-Runge-Lenz vector is also conserved.
Analytic Mechanics of Locally Conservative Physical Systems
The analysis of the dynamics of a material point perfectly constrained to a submanifold of the three-dimensional euclidean space and subjected to a locally conservative force's field, namely a force's field corresponding to a closed but not necessarily exact differential form on such a submanifold, requires a generalization of the Lagrangian and the Hamiltonian formalism that is here developed.
The mathematical role of (commutative and noncommutative) infinitesimal random walks over (commutative and noncommutative) riemannian manifolds in Quantum Physics
Anderson's nonstandard construction of brownian motion as an infinitesimal random walk on the euclidean line is generalized to an Hausdorff riemannian manifold. A nonstandard Feynman-Kac formula holding on such an Hausdorff riemannian manifold is derived. Indications are given on how these (radically elementary) results could allow to formulate a nonstandard version of Stochastic Mechanics (avoiding both the explicitly discussed bugs of Internal Set Theory as well as the controversial renormalization of the stochastic action). It is anyway remarked how this would contribute to hide the basic feature of Quantum Mechanics, i.e. the noncommutativity of the observables' algebra, whose structure is naturally captured in the language of Noncommutative Probability and Noncommutative Geometry. With this respect some preliminary consideration concerning the notion of infinitesimal quantum random walk on a noncommutative riemannian manifold, the notion obtained by the Sinha-Goswami's definition of quantum brownian motion on a noncommutative riemannian manifold replacing a continuous time interval with an hyperfinite time interval, is presented.
A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness
A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers. The notion of algorithmic-randomness is then extended to non-Dedekindian numbers. As a particular case, the notion of algorithmic randomness for the particular hyperreal number system of Non-Standard Analysis is explicitly analyzed.
There exist consistent temporal logics admitting changes of History
Introducing his Chronology Protection Conjecture Stephen Hawking said that it seems that there exists a Chronology Protection Agency making the Universe safe for historians. Without taking sides about such a conjecture we show that the Chronology Protection Agency is not necessary in order to make the Universe unsafe for historians but safe for logicians.
The multihistory approach to the time-travel paradoxes of General Relativity: mathematical analysis of a toy model
With a mathematical eye to Matt Visser's multihistory approach to the time-travel-paradoxes of General Relativity, a non relativistic toy model is analyzed in order of characterizing the conditions in which, in such a toy model, causation occurs.
Some elementary rigorous remark about the replica formalism in the Statistical Physics' approach to threshold phenomena in Computational Complexity Theory
Some elementary rigorous remark about the replica formalism in the Statistical Physics' approach to threshold phenomena in Computational Complexity Theory is presented.
A Gröenewald Van Hove like formulation of the ordering problems of General Relativity
A simple formal recasting of well known arguments concerning the ordering problems of General Relativity allows to obtain in such a context a Gröenewald Van Hove like theorem.
Renormalization Group versus Kolmogorov-Sinai entropy: a very simple remark
A very simple remark concerning a link between the notions of Kolmogorov-Sinai entropy and of Renormalization Group is performed.