| __Encyclopedia :: encyclopedia : Mathematical physics__ *(Site not responding. Last check: 2007-11-06)* |

| | 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 (SchrÃ¶dinger operators), including the connections to atomic and molecular physics. |

| | 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 mathematically rigorous physics research are functional analysis and probability **theory**. |

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