mathematical-physics

In 2009 Alday, Gaiotto and Tachikawa (AGT) conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of $N=2$ super-conformal field theory. I would like to know if anything similar shows up for WZW conformal blocks. A much more elementary (but related ) questio…

Mathematicians are like anatomists learning how a body works, or navigators charting new waters.

Forget solid, liquid, gas. This research used advanced math to theorize about topological phases of matter. And over the years experiments with matter and cold atoms have been validating the ideas.

AI-powered breakthroughs are raising big questions about how to do mathematics – and why we do it in the first place.

The Riemann Hypothesis (RH) has resisted resolution within classical mathematics for more than a century. This paper argues that RH cannot be settled by classical means because it is not an internal mathematical conjecture. Instead, RH expresses a generative constraint operating at the substrate level of the Assembled Mathematical Layer (AML), the mathematical world model produced under Generativ…

Two open problems, exact-arithmetic checking and a proof assistant, over a single weekend. The post Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming appeared first on Towards Data Science .

Hi all, I'm working on a numerical simulation involving the SSH model and the density matrix formalism. I'm using annihilation and creation operators at the first site, denoted by [itex]a_1[/itex] and [itex]a_1^\dagger[/itex], and I'm trying to understand how to construct and compute expressions like... Read more

Hello everyone, My name is Gautam Pal, and I am an independent researcher joining you from West Bengal, India. My primary fields of interest include theoretical physics, astro-mathematics, and cosmology. For a long time, I have been working independently on exploring the foundational mechanics... Read more

how it works A drumhead clamped at its rim can only vibrate in certain shapes, at certain frequencies. Those shapes and frequencies are the solutions of −∇²u = λu  inside the shape,  u = 0 on the edge Each solution u is a mode, a standing wave, and each λ gives a frequency proportional to √λ. This is an eigenvalue problem,…

The math, which combines chaos, quantum theory, and infinitely complex fractal structures, has been called a “foundational result.”

From 3-modules realized as sesquialgebra, bialgebras, Hopf algebra, quantum groups, fusion categories: Kevin Walker, On Witten’s 3-manifold invariants (1991) pdf Scott Carter, Louis Kauffman, Masahico Saito, Diagrams, Singularities, and Their Algebraic Interpretations, in “10th Brazilian Topology Meeting, S. Carlos, July 22 26, 1996 (pdf (dead)) Kursat Sozer, Alexis Virelizier, 3d TQFTs and 3-man…

Hello Physics Forums community!I'm an independent researcher with a background in mathematical modeling, field theory, and differential geometry. I'm joining PF to connect with the community, learn from ongoing discussions in theoretical physics and quantum field theory, and ask a few targeted... Read more