Mathematical physics is a research area focused on formulating and analyzing physical theories using rigorous mathematical structures and methods, and conversely, on developing new mathematics motivated by physical problems. It encompasses the study of quantum mechanics, quantum field theory, statistical mechanics, general relativity, and dynamical systems through functional analysis, operator algebras, differential geometry, probability theory, and partial differential equations. Core topics include spectral theory of Hamiltonians, rigorous renormalization, exactly solvable models, phase transitions, integrable systems, and geometric and topological methods in gauge theories and gravitation, with emphasis on precise definitions, theorems, and proofs underpinning fundamental physical concepts.
Adding one simple rule to an idealized game of billiards leads to a wealth of intriguing mathematical questions, as well as applications in the physics of living organisms. This week, researchers from the University of Amsterdam, ...
General Physics
Apr 11, 2024
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In a recent development at Fudan University, a team of applied mathematicians and AI scientists has unveiled a cutting-edge machine learning framework designed to revolutionize the understanding and prediction of Hamiltonian ...
General Physics
Feb 26, 2024
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For decades scientists have been trying to solve Feynman's Sprinkler Problem: How does a sprinkler running in reverse—in which the water flows into the device rather than out of it—work? Through a series of experiments, a ...
General Physics
Jan 29, 2024
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The branch of mathematics known as topology has become a cornerstone of modern physics thanks to the remarkable—and above all reliable—properties it can impart to a material or system. Unfortunately, identifying topological ...
General Physics
Jan 25, 2024
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Physicists and mathematicians from the Ural Federal University (UrFU) have created a complex mathematical model that calculates the distribution of nanoparticles (in particular, viruses) in living cells. The mathematical ...
Bio & Medicine
Sep 13, 2022
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88
Albert Einstein constructed equations of general relativity by adopting Riemann geometry. In addition to the key role it played in mathematics and physics, Riemann geometry has provided predictions for the properties of curved ...
Nanomaterials
Apr 4, 2022
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