Related papers: Group Theory in Physics: An Introduction with Math…
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
Building a consistent Quantum Theory of Gravity is one of the most challenging aspects of modern theoretical physics. In the past couple of years, new attempts have been made along the path of ``asymptotic safety'' through the use of Exact…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Traditionally, scholars in physics education research pay attention to students solving well-structured learning activities, which provide restricted room for collaboration and idea-generation due to their close-ended nature. In order to…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
I give a very brief introduction to the use of effective field theory techniques in quantum calculations of general relativity. The gravitational interaction is naturally organized as a quantum effective field theory and a certain class of…