Properties of non-hermitian quantum field theories
[Propriétés des théories des champs quantiques non hermitiens]
Bender, Carl M.1
1 Washington University, Department of Physics, Campus Box 1105, St. Louis, MO 63130 (USA)
Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 997-1008.

Dans cet article, je traite des systèmes quantiques dont l’hamiltonien est non-hermitien mais dont les niveaux d’énergie sont tous réels et positifs. De telles théories doivent être symétriques sous 𝒞𝒫𝒯, mais pas sous 𝒫 et 𝒯 séparément. Récemment, des systèmes quantiques avec de telles propriétés ont été étudiés en détail. Dans cet article, j’étends ces résultats aux théories des champs quantiques. Parmi les systèmes dont je parle, se trouvent les théories -φ 4 et iφ 3 . Toutes ces théories ont des propriétés inattendues et remarquables. Je décris les fonctions de Green qui apparaissent dans ces théories et je présente de nouveaux résultats concernant les états liés, la renormalisation et les calculs non-perturbatifs.

In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under 𝒞𝒫𝒯, but not symmetric under 𝒫 and 𝒯 separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are -φ 4 and iφ 3 theories. These theories all have unexpected and remarkable properties. I discuss the Green’s functions for these theories and present new results regarding bound states, renormalization, and nonperturbative calculations.

DOI : 10.5802/aif.1971
Classification : 34M60, 34B24, 34B40, 34L10
Keywords: ${\mathcal {C}}{\mathcal {P}}{\mathcal {T}}$, non-hermitian
Mot clés : ${\mathcal {C}}{\mathcal {P}}{\mathcal {T}}$, non-hermitien
Bender, Carl M. 1

1 Washington University, Department of Physics, Campus Box 1105, St. Louis, MO 63130 (USA) 
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Bender, Carl M. Properties of non-hermitian quantum field theories. Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 997-1008. doi : 10.5802/aif.1971. http://www.numdam.org/articles/10.5802/aif.1971/

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