Related papers: A moonshine dialogue in mathematical physics
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
There is a deep connection between cosmology -- the science of the infinitely large --and particle physics -- the science of the infinitely small. This connection is particularly manifest in neutron particle physics. Basic properties of the…
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
Bipartite graphs, especially drawn on Riemann surfaces, have of late assumed an active role in theoretical physics, ranging from MHV scattering amplitudes to brane tilings, from dimer models and topological strings to toric AdS/CFT, from…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
We point out an explicit connection between graphs drawn on compact Riemann surfaces defined over the field $\bar{\mathbb{Q}}$ of algebraic numbers --- so-called Grothendieck's {\it dessins d'enfants} --- and a wealth of distinguished…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
Many scientists seeking to understand the quantum mechanics of measurement situations (Copenhagen quantum theory) agree on its overwhelmingly successful algorithms to predict the outcomes of laboratory measurements but disagree on what…
Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix…
The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the infinite and finite volume respectively. It is found that there is a resonance state generated dynamically, which…
Reviewing the construction of induced representations of the Poincar\'e group of four-dimensional spacetime we find all massive representations, including the ones acting on interacting many-particle states. Massless momentum wavefunctions…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
We study the volume of the intersection of two unit balls from one of the classical matrix ensembles GOE, GUE and GSE, as the dimension tends to infinity. This can be regarded as a matrix analogue of a result of Schechtman and…
We present evidence for an undiscovered link between N=2 supersymmetric quantum field theories and the mathematical theory of helices of coherent sheaves. We give a thorough review for nonspecialists of both the mathematics and physics…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
The nature of the existence, revealed through Human cognitive system, has been evolving since the development of the languages. Part of such revelations were the geometrical forms and the numbers, whose beauty and order, wondrous and…
The Platonic solids is the name traditionally given to the five regular convex polyhedra, namely the tetradron, the octahedron, the cube, the icosahedron and the dodecahedron. Perhaps strongly boosted by the towering historical influence of…