Over a year ago, I wrote here about ice. It has 16 known forms with different…]]>

An interesting summary, by John Baez, of experimental findings and theoretical conjectures around the hydronium chemical structure.

Over a year ago, I wrote here about ice. It has 16 known forms with different crystal geometries. The most common form on Earth, hexagonal ice I, is a surprisingly subtle blend of order and randomness:

Liquid water is even more complicated. It’s mainly a bunch of molecules like this jostling around:

The two hydrogens are tightly attached to the oxygen. But accidents do happen. On average, for every 555 million molecules of water, *one* is split into a negatively charged OH⁻ and a positively charged H⁺. And this actually matters a lot, in chemistry. It’s the reason we say water has pH 7.

Why? By definition, pH 7 means that for every liter of water, there’s 10^{-7} moles of H⁺. That’s where the 7 comes from. But there’s 55.5 moles of water in every liter, at least when the water is cold so its density is almost…

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* * My first approach to the formal construction and properties of the Fock space as a Grad student was in a seminar intended to teach quantum mechanics to mathematicians, organized by Prof. Leonard Gross in the spring of 2011 at Cornell. In this seminar we went as far as to study *free fields* such as the electromagnetic field. And there, problems such as the popular

— that appears in many physics books in the quantization of the electromagnetic field — were solvable within the Fock space. Other topics were discussed as well, but they mostly served as a preparation for this topic. Here you have Prof. Gross’ lecture notes if you want to know more. This seminar took place a year after a special graduate course imparted by Prof. Garnett Chan about electronic structure in the Chemistry department, which included one modulus devoted to introduce several many-body techniques — such as green functions, Feymann diagrams, Wicks theorem and the Dyson equation and others– as they apply to quantum chemistry. Based on what I learned and judging by the great amount of literature that shows how effective these techniques are in the study of interacting systems, I find hard to understand how these two situations — the one described in the book mentioned above and the great success in the description of many real systems — can occur simultaneously. This apparent ambiguity is very common between science and math. It was always present while I was educated as a scientist.

I’m about to start reading the second part of the first chapter of Emch’s book, where the alternative and more algebraic approach to the description of systems with infinite degrees of freedom is introduced. I believe that what I’m about to learn is something well established among the experts. Certainly, I will enjoy and benefit from this reading. Alongside, I keep another great book: *Quantum theory of Many-Particle* *Systems* by Fetter and and Walecka. My hope is that together they will provide a good balance between the formal aspects and physical motivations. I’m planning on posting from what I learn as I progress on my reading.

The sea and the beach next to the scripps institute, San Diego CA.

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