**Axiomatic quantum field theory** is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective.

There are two main challenges in this discipline. First, one must propose a set of axioms which describe the general properties of any mathematical object that deserves to be called a "quantum field theory". Then, one give rigorous mathematical constructions of examples satisfying these axioms.

### Famous quotes containing the words theory, field, axiomatic and/or quantum:

“Psychotherapy—The *theory* that the patient will probably get well anyway, and is certainly a damned ijjit.”

—H.L. (Henry Lewis)

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—Walt Whitman (1819–1892)

“It is ... *axiomatic* that we should all think of ourselves as being more sensitive than other people because, when we are insensitive in our dealings with others, we cannot be aware of it at the time: conscious insensitivity is a self-contradiction.”

—W.H. (Wystan Hugh)

“A personality is an indefinite *quantum* of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite *quantum* of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”

—Hubert C. Heffner (1901–1985)