Mathematical physics

Mathematical physics is a scientific discipline aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. Mathematical physics covers a very broad area of topics with the common feature that they blend pure mathematics and physics. Although mathematical physics and theoretical physics are related, these two notions are often distinguished 1. Mathematical physics emphasizes the mathematical rigor of the same type as found in mathematics while theoretical physics emphasizes the links to observations and experimental physics which often requires the theoretical physicists to use heuristic, intuitive, and approximate arguments. Arguably, mathematical physics is closer to mathematics, and theoretical physics is closer to physics. Some compensation for the fact that mathematicians tend to call mathematical physicists 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.

Related Topics:
Physics - Framework - Mathematics - Theoretical physics - 1 - Rigor - Experimental physics - Heuristic - Intuitive

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Mathematical physicists primarily expand and elucidate physical theories. Because of the required rigor, mathematical physicists often deal with questions that theoretical physicists have considered to be solved. However, the mathematical physicists can sometimes show (but neither commonly nor easily) that the previous solution was incorrect.

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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. Quantum mechanics cannot be understood without a good knowledge of mathematics. It is not surprising, then, that its developed version under the name of quantum field theory is one of the most abstract, mathematically-based areas of the physical sciences, dealing with algebraic structures such as Lie Algebras - a topic of which ordinary physicists are often ignorant. Among the most relevant areas of contemporary mathematics in mathematical physics research are functional analysis and probability theory. Other subjects researched by mathematical physicists include operator algebras, geometric algebra, noncommutative geometry, string theory, group theory, random fields etc.

Related Topics:
Quantum field theory - Statistical mechanics - Phase transitions - Nonrelativistic quantum mechanics - Schrödinger - Operators - Atomic and molecular physics - Lie Algebra - Functional analysis - Probability theory - Operator algebra - Geometric algebra - Noncommutative geometry - String theory - Group theory - Random field

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James Clerk Maxwell, Lord Kelvin, and J. Willard Gibbs were mathematical physicists that had a profound impact on 19th century science. Revolutionary mathematical physicists at the turn of the 20th century include David Hilbert and almost all of the original founders of quantum mechanics. Other prominent mathematical physicists that transformed physics include Jules-Henri Poincaré and Satyendra Nath Bose.

Related Topics:
James Clerk Maxwell - Lord Kelvin - J. Willard Gibbs - 19th century - 20th century - David Hilbert - Jules-Henri Poincaré - Satyendra Nath Bose

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