Related papers: Introducing categories to the practicing physicist
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the…
We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…
Many instructors choose to assess their students using open-ended written exam items that require students to show their understanding of physics by solving a problem and/or explaining a concept. Grading these items is fairly time…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…
The well-known difficulties arising in a classification which is not set-theoretically trivial---involving what is sometimes called a non-smooth quotient---have been overcome in a striking way in the theory of operator algebras by the use…
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…
It is becoming increasingly difficult for geometers and even physicists to avoid papers containing phrases like `triangulated category', not to mention derived functors. I will give some motivation for such things from algebraic geometry,…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
We give a new construction of the algebraic $K$-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and…
"So what do you do? I mean, what do you actually do?" This is one of the most common questions one theoretical physicist receives from her students, and is representative of a common curiosity among aspiring physicists. Students often…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
In recent years, computing has become an important part of the way we teach and learn physics. Teachers, both at high school and college levels, now use computational activities in many of their courses. Physics departments are offering…
This is a pedagogical introduction to the treatment of general relativity as a quantum effective field theory. Gravity fits nicely into the effective field theory description and forms a good quantum theory at ordinary energies.
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…