We discuss second quantization, discrete symmetry transformations, and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons.
机构:
Kings Coll London, Dept Phys, London WC2R 2LS, EnglandKings Coll London, Dept Phys, London WC2R 2LS, England
Alexandre, Jean
;
Bender, Carl M.
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Kings Coll London, Dept Phys, London WC2R 2LS, England
Washington Univ, Dept Phys, St Louis, MO 63130 USAKings Coll London, Dept Phys, London WC2R 2LS, England
Bender, Carl M.
;
Millington, Peter
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Tech Univ Munich, Phys Dept T70, D-85748 Garching, GermanyKings Coll London, Dept Phys, London WC2R 2LS, England
机构:
Univ Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, JapanUniv Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
Ashida, Yuto
;
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机构:
Furukawa, Shunsuke
;
Ueda, Masahito
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Univ Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
RIKEN, CEMS, Wako, Saitama 3510198, JapanUniv Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
机构:
Kings Coll London, Dept Phys, London WC2R 2LS, EnglandKings Coll London, Dept Phys, London WC2R 2LS, England
Alexandre, Jean
;
Bender, Carl M.
论文数: 0引用数: 0
h-index: 0
机构:
Kings Coll London, Dept Phys, London WC2R 2LS, England
Washington Univ, Dept Phys, St Louis, MO 63130 USAKings Coll London, Dept Phys, London WC2R 2LS, England
Bender, Carl M.
;
Millington, Peter
论文数: 0引用数: 0
h-index: 0
机构:
Tech Univ Munich, Phys Dept T70, D-85748 Garching, GermanyKings Coll London, Dept Phys, London WC2R 2LS, England
机构:
Univ Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, JapanUniv Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
Ashida, Yuto
;
论文数: 引用数:
h-index:
机构:
Furukawa, Shunsuke
;
Ueda, Masahito
论文数: 0引用数: 0
h-index: 0
机构:
Univ Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan
RIKEN, CEMS, Wako, Saitama 3510198, JapanUniv Tokyo, Dept Phys, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1130033, Japan