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Mathematical Physics Lab
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A lab that solves mathematical problems originating in physics using analytic methods.
AboutAbout the lab
Solving mathematical problems born from physics.
The field of mathematical physics here studies mathematical problems that originate in quantum field theory, statistical mechanics, and fluid dynamics.
It aims to solve these problems using analytic methods such as functional analysis and probability theory.
It is not bound by existing methodologies, and where necessary also aims to develop new mathematics.
The research areas of the faculty members include quantum field theory, spectral analysis, quantum topology, and optimal transport theory.
Key terms
- Quantum field theory
- A theory that applies the ideas of quantum mechanics to "fields," such as the electromagnetic field.
- Functional analysis
- A branch of mathematics that studies spaces whose elements are functions, and the operators acting on those spaces.
- Spectral analysis
- A mathematical method for studying the properties of the values (the spectrum) that an operator can take.
- Quantum invariant
- A quantity, defined by methods derived from quantum theory, that is used to distinguish knots and 3-manifolds.
ResearchResearch themes
The lab aims to solve mathematical problems originating in quantum field theory, statistical mechanics, and fluid dynamics using analytic methods such as functional analysis and probability theory. The faculty introduction on the field's page lists quantum field theory, partial differential equations, quantum topology, and optimal transport theory, among others, as research areas.
*Illustrative imageSolving Physics-Originated Problems with Analysis
The lab aims to solve mathematical problems originating in quantum field theory, statistical mechanics, and fluid dynamics using analytic methods such as functional analysis and probability theory. Where necessary, it also aims to develop new mathematics.
*Illustrative imageSpectral Analysis in Quantum Field Theory
Professor Fumio Hiroshima investigates the spectra of operators on infinite-dimensional spaces. Ground states and other properties of Hamiltonians arising in quantum field theory are analyzed using operator theory, stochastic analysis, functional integrals, and related tools.
*Illustrative imageQuantum Topology
Associate Professor Kazuhiro Hikami studies quantum invariants of knots and 3-manifolds, including their connections to double affine Hecke algebras and skein algebras.
MembersFaculty
- ProfessorFumio Hiroshima
- ProfessorTakaharu Yaguchi
- Associate ProfessorKoichi Taira
- Associate ProfessorKazuhiro Hikami
- Associate ProfessorToshiaki Yachimura
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Crabbers eye knot-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Solving Physics-Originated Problems with Analysis: “The board” Yulia Meshkova / CC BY 4.0 (cropped)
- Spectral Analysis in Quantum Field Theory: “Light spectrum on a wall caused by sunlight going through prism and then handmade glass” Pittigrilli / CC BY-SA 4.0 (cropped)
- Quantum Topology: “Twist braid knot” Zaripov Rustem / CC BY-SA 4.0 (cropped)
- Related lab (Dynamical Systems Lab): “Lorenz caos3” António Miguel de Campos / Public domain (cropped)
- Related lab (Optimization Lab): “Undirected NetworkX Graph” KalebD07 / CC0 (cropped)
- Related lab (Mathematical Cryptography Lab): “Enigma Machine (Bletchley Park) - Flickr - Tim Gage” Tim Gage / CC BY-SA 2.0 (cropped)
- Related lab (Infinite-Dimensional Integrable Systems Lab): “Jeff Rowley Big Wave Surfer Jaws line up 2 Peahi Maui by Xvolution Media - Flickr - Jeff Rowley Big Wave Surfer” Jeff Rowley / CC BY 2.0 (cropped)
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