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We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilberts 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables starting at two loops for eight particles.
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohrs idea that the empirical content of quantum physics is accessible only through
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of
Here we deal in a pedagogical way with an approach to construct an algebraic structure for the Quantum Mechanical measurement processes from the concept of emph{Measurement Symbol}. Such concept was conceived by Julian S. Schwinger and constitutes a
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and r