Mathematical Physics (Books)

Mathematical Physics (Books) app - The mathematical physics group is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as quantum mechanics (both nonrelativistic and relativistic), atomic and molecular physics, disorder effects in condensed matter, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis, algebra and modern probability theory, to which such subjects lead.

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

mathematical physics, Branch of mathematical analysis that emphasizes tools and techniques of particular use to physicists and engineers. It focuses on vector spaces, matrix algebra, differential equations (especially for boundary value problems), integral equations, integral transforms, infinite series, and complex variables. Its approach can be tailored to applications in electromagnetism, classical mechanics, and quantum mechanics.

Mathematical physics applies rigorous mathematical ideas to problems inspired by physics. As such, it is a remarkably broad subject.

Mathematics and Physics are traditionally tightly linked subjects, and many historical figures such as Newton and Gauss were both physicists and mathematicians. Traditionally mathematical physics has been quite closely associated to ideas in calculus, particularly those of differential equations. In recent years however, in part due to the rise of superstring theory, many more branches of mathematics have become major contributors to physics.

At Duke, some of the mathematical physics studied is related to geometric ideas. For example, Hubert Bray uses geometric tools like minimal surfaces and harmonic functions to study gravity, black holes, and the curvature of spacetime. He is also interested in dark matter, which makes up most of the mass of galaxies, and which could just as reasonably be called the "large scale unexplained curvature of the universe."

As well as differential geometry, the subject of algebraic geometry now has many applications in mathematical physics. Paul Aspinwall is a string theorist who wields algebraic geometry to study the higher-dimensional spaces (and their compactification to the more familiar four dimensional spacetimes) which are string theories candidates for the physical universe.

Mark Stern employs geometry and partial differential equations to study Yang Mills theory, which is both the mathematical model describing the fundamental nuclear forces and a major tool of geometry and topology.

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