# Arthur Wightman

**Arthur Strong Wightman** (March 30, 1922 – January 13, 2013) was an American mathematical physicist. He was one of the founders of the axiomatic approach to quantum field theory, and originated the set of Wightman axioms.^{[1]}^{[2]}

Arthur Strong Wightman | |
---|---|

Born | |

Died | January 13, 2013^{[1]} | (aged 90)

Nationality | U.S. |

Alma mater | Yale University (B.A., 1942) Princeton University (Ph.D, 1949) |

Known for | Quantum field theory Wightman axioms |

Awards | Heineman Prize (1969) Henri Poincaré Prize (1997) |

Scientific career | |

Fields | Physicist |

Institutions | Yale University (1943-44) Princeton University (1949-71) |

Doctoral advisor | John Archibald Wheeler |

Doctoral students | Eduard Prugovecki Arthur Jaffe Barry Simon Alan Sokal Silvan S. Schweber Jerrold Marsden Oscar Lanford |

## Contents

## BiographyEdit

Advised by John Wheeler, Wightman's 1949 Princeton doctoral dissertation was entitled *The Moderation and Absorption of Negative Pions in Hydrogen*. His graduate students include Arthur Jaffe, Jerrold Marsden, and Alan Sokal. His work is summarized in the classic concise monograph *PCT, Spin and statistics and all that* written with R. F. Streater. Its title is a play on *1066 and All That*, the historical satire by Sellar and Yeatman. The PCT refers to the combined symmetry of a quantum field theory under P Parity, C charge and T time. Spin and statistics refers to the fact that in quantum field theory it can be proved that spin 1/2 particles obey Fermi–Dirac statistics whereas integer spin 0, 1, 2 particles obey Bose–Einstein statistics.^{[3]}

Wightman was awarded the Henri Poincaré Prize of the International Association of Mathematical Physics in 1997. Until his death, he was a professor emeritus at Princeton.

## WorksEdit

- R. F. Streater and Arthur Wightman:
*PCT, spin and statistics, and all that*, Princeton University Press 2000 (1st edn., New York, Benjamin 1964)^{[4]} - Arthur Wightman:
*Quantum field theory in terms of vacuum expectation values*. In:*Physical Review*. vol. 101, 1956, p. 860 - Arthur Wightman and Lars Gårding:
*Fields as operator-valued distributions in relativistic quantum theory*. In:*Arkiv för Fysik*. vol. 28, 1965, pp. 129–184 - Arthur Wightman:
*What is the point of so-called "axiomatic field theory"?*. In:*Physics Today*. September 1969 - Arthur Wightman
*Introduction to some aspects of the relativistic dynamics of quantized fields*, in Maurice Lévy (ed.)*High energy electromagnetic interactions and field theory*, Cargèse Summer School 1964, Gordon and Breach, New York 1967 - Arthur Wightman:
*Should we believe in Quantum Field Theory?*. In: Zichichi (ed.):*The Whys of subnuclear physics*. In:*Ettore Majorana Course*. vol. 19, 1975, p. 983 - Arthur Wightman, Wick and Wigner:
*Intrinsic parity of elementary particles*. In:*Physical Review*. vol. 88, 1952, p. 101 - Arthur Wightman:
*Looking back at Quantum Field Theory*. In:*physica scripta*. vol. 24, 1981, p. 813 - Res Jost:
*To Arthur Wightman*. In:*Communications in mathematical physics*. vol. 132, 1990, p. 1 - Arthur Wightman:
*The theory of quantized fields in the 50s*, in Brown, Dresden, Hoddeson (eds.)*Pions to quarks: particle physics in the 50s*, Cambridge University Press 1989

## ReferencesEdit

- ^
^{a}^{b}Kelly, Morgan (2013-01-30). "Princeton University - Esteemed Princeton mathematical physicist and mentor Arthur Wightman dies". Princeton.edu. Retrieved 2013-02-13. **^**Simon, Barry, ed. (March 2015). "In Memory of Arthur Strong Wightman" (PDF).*Notices of the AMS*.**62**(3): 249–257.**^**Jaffe, Arthur; Simon, Barry. "Arthur Strong Wightman (1922–2013)". International Association of Mathematical Physics News Bulletin. Retrieved 25 March 2013.**^**Ruelle, D. (1965). "Review: R. F. Streater and A. S. Wightman,*PCT, Spin and statistics, and all that*".*Bull. Amer. Math. Soc*.**71**(1): 130–132. doi:10.1090/s0002-9904-1965-11247-2.