Renormalization group | Scaling symmetries
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation. The renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (so-called self-similarity). As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable couplings which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances. For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the dressed electron seen at large distances, and this change, or running, in the value of the electric charge is determined by the renormalization group equation. (Wikipedia).
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
In this veideo we continue our look in to the dihedral groups, specifically, the dihedral group with six elements. We note that two of the permutation in the group are special in that they commute with all the other elements in the group. In the next video I'll show you that these two el
From playlist Abstract algebra
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Michael Wibmer: Etale difference algebraic groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Group Theory II Symmetry Groups
Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of
From playlist Foundational Math
Visual Group Theory, Lecture 2.2: Dihedral groups
Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota
From playlist Visual Group Theory
Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (1/4)
In physics, the renormalisation group provides a powerful point of view to understand random systems with strong correlations. Despite advances in a number of particular problems, in general its mathematical justification remains a holy grail. I will give an introduction to the main concep
From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective
Renormalization Group Flows and the $a$-theorem by John Cardy
Date : Wednesday, July 5, 2017 Time : 16:15 PM Venue : Ramanujan Lecture Hall, ICTS Campus, Bangalore Abstract : In 1986 A Zamolodchikov derived the remarkable result that in two-dimensional quantum field theories renormalization group flows are irreversible. T
From playlist Seminar Series
Roland Bauerschmidt - Perspectives on the renormalisation group approach
The goal of this talk is to review some of the successes but also the outstanding challenges of the renormalisation group approach to the Ising and \varphi^4 models. I will also try to describe a common perspective of the usual approach to the renormalisation group based on perturbation th
From playlist 100…(102!) Years of the Ising Model
Curvature function renormalisation and topological phase transitions by Sumathi Rao
DISCUSSION MEETING NOVEL PHASES OF QUANTUM MATTER ORGANIZERS: Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara DATE: 23 December 2019 to 02 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Recent theoretical and experimental
From playlist Novel Phases of Quantum Matter 2019
Daniel Friedan - Where does quantum field theory come from?
Daniel Friedan (Rutgers Univ.) Where does quantum field theory come from? This will be an interim report on a long-running project to construct a mechanism that produces spacetime quantum field theory; to indentify possible exotic, non-canonical low- energy phenomena in SU(2) and SU(3) gau
From playlist Conférence à la mémoire de Vadim Knizhnik
Roland Bauerschmidt: Lecture #2
This is a second lecture on "Log-Sobolev inequality and the renormalisation group" by Dr. Roland Bauerschmidt. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
Group theory 13: Dihedral groups
This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.
From playlist Group theory
Strong-coupling renormalization group in the hierarchical Kondo model - Ian Jauslin
Topic: Strong-coupling renormalization group in the hierarchical Kondo model Speaker: Ian Jauslin, Member, School of Mathematics Time/Room: 4:15pm - 4:30pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Roland Bauerschmidt: Log-Sobolev inequality for the continuum Sine-Gordon model
The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations. Abstract: We derive a multiscale generalisation of the Bakry–Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an
From playlist Workshop: Workshop: Singular SPDEs and Related Topics
Werner Müller : Analytic torsion for locally symmetric spaces of finite volume
Abstract : This is joint work with Jasmin Matz. The goal is to introduce a regularized version of the analytic torsion for locally symmetric spaces of finite volume and higher rank. Currently we are able to treat quotients of the symmetric space SL(n,ℝ)/SO(n) by congruence subgroups of SL(
From playlist Topology
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Renormalization: The Art of Erasing Infinity
Renormalization is perhaps one of the most controversial topics in high-energy physics. On the surface, it seems entirely ad-hoc and made up to subtract divergences which appear in particle physics calculations. However, when we dig a little deeper, we see that renormalization is nothing t
From playlist Standard Model
The Special Linear Group is a Subgroup of the General Linear Group Proof
The Special Linear Group is a Subgroup of the General Linear Group Proof
From playlist Abstract Algebra