Some basic properties of infinite dimensional Hamiltonian systems

We consider some fundamental properties of infinite dimensional Hamiltonian systems, both linear and nonlinear. For exemple, in the case of linear systems, we prove a symplectic version of the teorem of M. Stone. In the general case we establish conservation of energy and the moment function for system with symmetry. (The moment function was introduced by B. Kostant and J .M. Souriau). For infinite dimensional systems these conservation laws are more delicate than those for finite dimensional systems because we are dealing with partial as opposed to ordinary differential equations

Quantum Canonical Transformations revisited

A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.Comment: 8 pages, LaTe

On the Groenewold-Van Hove problem for R^{2n}

We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve it when n = 1. We rigorously show that there exists an obstruction to quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap in Groenewold's original proof without introducing extra hypotheses. Moreover, when n = 1 we determine the largest Lie subalgebras of polynomials which can be unambiguously quantized, and explicitly construct all their possible quantizations.Comment: 15 pages, Latex. Error in the proof of Prop. 3 corrected; minor rewritin

Numberlines: Hockey Line Nicknames Based on Jersey Numbers

The purpose of this article, in general, is to expound Chernoff’s (2016) notion of numberlines, that is, hockey line nicknames based on jersey numbers. The article begins with a brief discussion of the history of hockey line nicknames, which allows for the parsing of numberlines and quasi-numberlines (nicknames based on numbers associated with hockey players). Focusing, next, on jersey number restrictions for the National Hockey League (NHL), a repeated calculation of the number of possible numberlines winnows down the number from a theoretical upper bound to a practical upper bound. Moving beyond the numbers, the names of natural numbers – those with a certain panache (e.g., Untouchable, McNugget, Frugal, Hoax, Narcissistic, Unhappy, Superperfect and Powerul numbers) – act as a gateway to the notion of numberlining, the process of attempting to coin a numberline. Two particular examples, The Powers Line and The Evil Triplets provide a window into the process of numberlining. Prior to concluding remarks, which explain how numberlines and numberlining fall in line with the NHL’s recent embrace of fans’ use of social media, the article details how adopting hockey line nicknames based on jersey numbers can be used as a possible venue to rename questionable hockey line nicknames

Lessons Learned from the Disorder of Operations

The purpose of this article, in general, is to explore certain possible outcomes associated with an underaged gambler attempting to collect his rightful winnings. More specifically, this article is a thought experiment investigating the union of (1) skill testing questions, (2) the equation that recently broke/divided the internet, and (3) how different outcomes render different elements of the thought experiment moot. For example, when the final arbiter has total dominion over a particular outcome, the mathematics of a skill testing question is rendered moot. The article concludes with a discussion revealing how disorder of operations could be considered the teaching and learning of mathematics version of other famous controversial issues (e.g., gun control, animal rights, welfare, etc.) found in society

Solving Equations: A Make-Work Project for Math Teachers and Students

The purpose of this article is to share a particular view that I have towards solving equations in the school mathematics classroom. Specifically, I contend that solving equations in the math classroom is a make-work project for math teachers and students. For example, math teachers take a predetermined value that makes a statement true, and then proceed to make it harder and harder and harder for their students to determine the value that makes the statement true. However, math teachers do so with the explicit purpose of teaching their students how to reveal the solution that they themselves have concealed. Stated in make-work project parlance, the math teacher digs a hole with the explicit purpose of teaching, then having the students fill the hole that they dug