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.
From the early days of quantum mechanics, scientists have thought that all particles can be categorized into one of two groups—bosons or fermions—based on their behavior.
Condensed Matter
Jan 8, 2025
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A research team has experimentally calculated the Jones polynomial based on the quantum simulation of braided Majorana zero modes. The research team determined the Jones polynomials of different links through simulating the ...
Quantum Physics
Dec 30, 2024
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208
Skoltech researchers have proposed novel mathematical equations that describe the behavior of aggregating particles in fluids. This bears on natural and engineering processes as diverse as rain and snow formation, the emergence ...
General Physics
Dec 23, 2024
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114
String theory, conceptualized more than 50 years ago as a framework to explain the formation of matter, remains elusive as a "provable" phenomenon. But a team of physicists has now taken a significant step forward in validating ...
General Physics
Dec 17, 2024
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170
Theoretical physicists have established a close connection between the two rapidly developing fields in theoretical physics, quantum information theory and non-invertible symmetries in particle and condensed matter theories, ...
Condensed Matter
Nov 29, 2024
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A team of engineers and mathematicians from ETH Zürich, working with colleagues from The Institute of Statistical Mathematics, and ATR Institute International, both in Japan, has successfully modeled the physics involved ...
Dr. Asela Abeya, of SUNY Poly faculty in the Department of Mathematics and Physics, has collaborated with peers at the University at Buffalo and Rensselaer Polytechnic Institute on a research paper titled "On Maxwell-Bloch ...
General Physics
Aug 1, 2024
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An international team of physicists, centered at Trinity, has proven new theorems in quantum mechanics that describe the "energy landscapes" of collections of quantum particles.
Condensed Matter
Jul 17, 2024
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141
While investigating how string theory can be used to explain certain physical phenomena, scientists at the Indian Institute of Science (IISc) have stumbled upon on a new series representation for the irrational number π. ...
General Physics
Jun 18, 2024
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2021
Scientists have used computational algebraic geometry to study predictions for particle physics experiments, such as those at the Large Hadron Collider (LHC), which first detected the Higgs particle in 2012.
General Physics
Jun 7, 2024
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