Knot means either a knot or a link preamble thinking outside the box knot theory quantum mechanics is a tool for exploring objectives we seek to define a quantum knot in such a way as to represent the state of the knotted rope, i. In mathematical language, a knot is an embedding of a circle in 3dimensional euclidean space, r 3 in. Mtheory is a theory in physics that unifies all consistent versions of superstring theory. Knot theory is the mathematical branch of topology that studies mathematical knots, which are defined as embeddings of a circle in 3dimensional euclidean space, r3.
Particle physics studies the smallest pieces of matter. Elementary particle physics from theory to experiment. These notes summarize the lectures delivered in the v mexican school of particle physics, at the university of guanajuato. The steps are understandable to high school students. The international conference knot theory and related topics received the worlds first was held at osaka as a satellite conference of icm kyoto in 1990, from whose proceedings knots 90 a. Shortly afterwards, in 1938, majorana mysteriously disappeared, and for 70 years his modified equation remained a rather obscure footnote in theoretical physics box 1. Edward witten first conjectured the existence of such a theory at a stringtheory conference at the university of southern california in the spring of 1995. Simons form, the jones polynomial and other notions of knot theory seem to play in. This knot has all features of an elementary particle, and behaves like an elementary particle with descrte mass and spin, in spite. Elementary particle physics from theory to experiment carlos wagner physics department, efi and kicp, univ.
This is a bit out there, but if you take a knot you can translate it into a graph and then translate the graph into a lattice described by statistical mechanics. This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasiphysical process. We also discuss knot theory in modern physics where it has found use in particle physics to describe the energy levels of glueballs in the form of knotted and linked tubes, and we introduce a. Applied physics topological mechanics of knots and tangles. In previous papers we have described quantum mechanics as a matrix symplectic geometry and showed the existence of a braiding and hopf algebra structure behind our lattice quantum phase space. While these subjects are very important to modern mathematics, learning them is a major undertaking. Antiparticles were predicted in 1930 by dirac, and discovered 2 years later e2 4. Applied physics topological mechanics of knots and tangles vishal p. In quantum physics, a knot may be regarded as the orbit in spacetime of a charged particle. In this work representing also enlarge version of 18 our preliminary article knot theory and particle physics published in the proceed.
Knot theory is a branch of topology that deals with study and classification of closed loops in 3d euclidean space. We give a survey of the application of ashtekars variables to the quantization of general relativity in four dimensions with special emphasis on the application of techniques of analytic knot theory to the loop representation. This paper is an introduction to relationships between knot theory and theoretical physics. March 2, 2015 abstract we use the assumptions of knot physics to prove that a collection of interacting neutrinos and antineutrinos maximize their quantum probability when all neutrinos are of the same helicity and all antineutrinos are of the opposite helicity. But perhaps the most interesting knot in physics is the electromagnetic knot in maxwells theory which can be viewed as electromagnetic geon. In this paper, we will describe a topological model for elementary particles based on 3manifolds. The rise of string theory, the fall of a science, and what comes next is a book about the history of physics from copernicus forward. The authors explain the principal concepts of perturbative field theory and demonstrate their application in practical situations. Pdf loops, knots, gauge theories and quantum gravity. A fundamental problem in knot theory is determining when two knots are the same, which leads to the study of knot invariants, such as knot polynomial.
Quantum mechanics, knot theory, and quantum doubles. Knots and quantum theory natural sciences institute for. Creation and control of knots in physical systems is the pinnacle of technical expertise, pushing forward stateoftheart experimental approaches as well as theoretical understanding of topology in selected medium. Applications to knot theory, word problems and to statistical mechanics are indicated. Knot physics a unification theory by caltech alumni a unification theory by caltech alumni. Group theory and symmetries in particle physics authors. Andrew the first called georgian university of the patriarchy of georgia. One way of calculating the jones polynomial in quantum theory involves using the chernsimons function for gauge fields. In topology, knot theory is the study of mathematical knots.
Moreover, faint shadows of kelvins original idea have been argued to be visible in string theory. We give an exposition of the theory of polynomial invariants of knots and links, the witten functional integral formulation of knot and link invariants, and the beginnings of topological quantum field theory, and show how the theory of knots is related to a number of key issues in mathematical physics. The scottish mathematical physicists referred to in the title are thomson. Kauffmann, knots and physics, world scientific publishers 1991 l. Then if you write the partition function of the lattice it will be an invariant of the knot.
Introduction knot theory is a theory studying the macroscopic physical phenomena of strings embedded in threedimensional space. The usual textbook approach to particle physics proceeds through quantum eld theory and gauge the ory. The author takes a primarily combinatorial stance toward. As a literal theory of physics the vortex atom hypothesis lasted no more than 30 years, even thomson himself giving up on it by 1890 krage 02, p. Electroweak unification is a consequence of including knot geometry in the description of the electromagnetic field. Below we will describe this standard model and its salient features. I want to do a little bit preparation before attending the lecture, so i would like to know what knot theory is. This ar ticle is an intr oduction to relationships betwe en knot the or y and the oretic al physics. But to use the chernsimons function, the knot must be a path in a spacetime of three dimensions two space dimensions and one time.
Standard model and grand uni ed theories is quite striking. Part of the students attending the lecture will be high school students like me. There is a natural connection between particle physics and representation theory, as first noted in the 1930s by eugene wigner. This text provides a selfcontained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. It is also a book that discusses the current state of physics research, particularly the dominion that string theory holds over the field. It links the properties of elementary particles to the structure of lie groups and lie algebras. The material presented in this book has been tested. Quantum mechanics is a consequence of the interactions of the branches of the. And the role of particle physics is to test this model in all conceivable ways, seeking to discover whether something more lies beyond it. In particular, hyperbolic 3manifolds have a close connection to number theory bloch group, algebraic ktheory, quaternionic trace. Apart from their generic relationship to knots and their application to particle physics 1, flattened moebius strips fms are of intrinsic interest as elements of a genus with specific rules of combination and a unique taxonomy. Today, the standard model is the theory that describes the role of these fundamental particles and interactions between them. Group theory and its applications in physics boris gutkin faculty of physics, university duisburgessen. D 2 of a knot k carrying a hyperbolic geometry and bosons as torus bundles.
One real particle has one knot on every branch of the manifold. Knots and quantum theory institute for advanced study. An overview of the entire theory, from simple assumptions about the spacetime manifold through particles. Particle physics and representation theory wikipedia.
Sandt 2, mathias kolle, jorn dunkel knots play a fundamental role in the dynamics of biological and physical systems, from dna to turbulent. We also discuss knot theory in modern physics where it has found use in particle physics to describe the energy levels of glueballs in the form. Modern physics demonstrates that the discrete wavelengths depend on quantum. Quantum knots an intuitive overview of the theory of. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone, the simplest knot being a ring or unknot. If a particle and antiparticle come across each other, they annihilate. Wittens announcement initiated a flurry of research activity known as the second superstring revolution. Although the subject matter of knot theory is familiar to everyone and its problems are easily stated, arising not only in many branches of mathematics but also in such diverse. Knot physics is the theory of the universe that not only unified all the. The demands of knot theory, coupled with a quantumstatistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The researchers say that the connection was unexpected because particle physics seemed far removed from knot theory, a branch of topology, the study of the properties of space and shapes. The first aim of this work is to give the defining commutation relations of the quantum weylschwingerheisenberg group associated with our. Knot physics assumes a branched 4manifold embedded in a 6dimensional minkowski space.