Related papers: A moonshine dialogue in mathematical physics
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard…
The classical theory of monstrous moonshine describes the unexpected connection between the representation theory of the monster group $M$, the largest of the simple sporadic groups, and certain modular functions, called Hauptmodln. In…
The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane. In a recent paper [arXiv:1503.08812] a new…
In a letter to Born, Einstein wrote: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the old one. I, at…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the $relational$ perspective on the theory, and a comment on its philosophical implications.
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
The behaviour of baby universes has been an important ingredient in understanding and quantifying non-critical string theory or, equivalently, models of two-dimensional Euclidean quantum gravity coupled to matter. Within a regularized…
These lectures study two correspondences between gauge theories and integrable many-body systems. The first arises from infinite-dimensional Hamiltonian reduction and relates gauge-theoretic dynamics directly to Calogero--Moser-type systems…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the…
Dessin d'enfants (French for children's drawings) serve as a unique standpoint of studying classical complex analysis under the lens of combinatorial constructs. A thorough development of the background of this theory is developed with an…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…