Open AccessCryptoreality of nonanticommutative Hamiltonians
Author(s) -
Evgeny Ivanov,
Andrei Smilga
Publication year - 2007
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2007/07/036
Subject(s) - minkowski space , supersymmetry , hermitian matrix , matrix similarity , mathematical physics , transformation (genetics) , class (philosophy) , theoretical physics , quantum field theory , physics , quantum , field (mathematics) , space (punctuation) , pure mathematics , algebra over a field , mathematics , quantum mechanics , computer science , biochemistry , chemistry , artificial intelligence , partial differential equation , gene , operating system
15 pages, 2 figuresWe note that, though nonanticommutative (NAC) deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of "cryptoreal'' Hamiltonians considered recently by Bender and collaborators. They can be made manifestly Hermitian via the similarity transformation H -> exp{R} H exp{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one, though being realized differently on the involved canonical variables. Besides quantum-mechanical models, we treat, along similar lines, some NAC deformed field models in 4D Minkowski space
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