Group of Mathematical Physics
Domingos Humberto Urbano Marchetti
João Carlos Alves Barata
Paulo Teotônio Sobrinho
Walter Alberto Siqueira Pedra
Mathematical Physics is a research area in Theoretical Physics whose main characteristic is the intense use of mathematical instruments and methods, working under the same logical standards in demonstrations as those commonly used in Mathematics. It aims to provide Theoretical Physics with more clear and precise deductive arguments and with more powerful mathematical tools for the formulation of physical theories and for the deduction and computation of properties of established
theories and models.
According to this view, Mathematical Physics is not limited in its range of physical interests, and encompasses many research directions in Theoretical Physics. Among others, one should mention Classical and Quantum Statistical Mechanics, Quantum Field Theory, Quantum Mechanics, Classical Mechanics and General Relativity.
The mathematical instruments typically required in the research work in Mathematical Physics come from many traditional areas of Mathematics, ranging from Analysis, Functional Analysis, Operator Algebras, Convex Analysis, Topology, Differential Geometry, Probability Theory, the Theory of Stochastic Processes, the Theory of Differential Equations, Group Theory, etc. Historically, Mathematical Physics contributed in many degrees to the development of these areas of Mathematics and this fruitful dialogue is preserved to this day.