| Mathematical Physics |
Article Index for Mathematical |
Website Links For Mathematical Physics |
Information AboutMathematical Physics |
| CATEGORIES ABOUT MATHEMATICAL PHYSICS | |
| mathematical physicsmathematical physics | |
| theoretical physics | |
| mathematics | |
| physics | |
| interdisciplinary fields | |
|
Using the tools and standards of rigor of contemporary mathematics, mathematical physicists study problems of modern theoretical physics. Mathematical physicists primarily elucidate physical Theories . Because of the required rigor, mathematical physicists often deal with questions that theoretical physicists have considered to already be solved. However, they can sometimes show (but neither commonly nor easily) that the previous solution was incorrect. Some compensation for the fact that mathematicians tend to call them physicists and that physicists tend to call them mathematicians is provided by the breadth of physical subject matter and beauty of various unexpected interconnections in the mathematical structure of rather distinct physical situations. The field has concentrated in three main areas: (1) Quantum Field Theory , especially the precise construction of models; (2) Statistical Mechanics , especially the theory of Phase Transitions ; and (3) Nonrelativistic Quantum Mechanics ( Schrödinger Operators ), including the connections to Atomic And Molecular Physics . The effort to put physical theories on a mathematically rigorous footing has inspired many mathematical developements. For example, the development of quantum mechanics and some aspects of Functional Analysis parallel each other in many ways. The mathematical study of quantum statistical mechanics has motivated results in Operator Algebras . The attempt to construct a rigorous quantum field theory has brought about progress in fields such as Representation Theory . Use of Geometry and Topology plays an important role in String Theory . The above are just a few examples. An examination of the current research literature would undoubtedly give other such instances. ALTERNATIVE MEANING In some cases, the term 'mathematical physics' is used synonymously with Theoretical Physics and herein refers to "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 " 1 . It can be seen as underpinning both Theoretical Physics and Computational Physics . PROMINENT MATHEMATICAL PHYSICISTS The great 17th century physicist Isaac Newton developed a wealth of new mathematics, in an informal way, to solve problems in physics, including a form of Calculus and Numerical Methods such as Newton's Method . James Clerk Maxwell , Lord Kelvin , William Rowan Hamilton , and J. Willard Gibbs were mathematical physicists who had a profound impact on 19th Century science. Revolutionary mathematical physicists at the turn of the 20th Century included David Hilbert who devised the theory of Hilbert Spaces for Integral Equations , to find a major application in Quantum Mechanics . The "very mathematical" Paul Dirac used algebraic constructions to produce a relativistic model for the electron, predicting its Magnetic Moment and the existence of its antiparticle, the Positron . Albert Einstein 's Special Relativity replaced the Galilean Transformations of space and time with Lorentz Transformations , and his General Relativity replaced the flat geometry of the large scale universe by that of a Riemannian Manifold , whose curvature replaced Newton's gravitational force. Other prominent mathematical physicists include Jules-Henri Poincaré and Satyendra Nath Bose . NOTES
BIBLIOGRAPHICAL REFERENCES
SEE ALSO EXTERNAL LINKS
|
|
|