The C operator in PT -symmetric quantum field theory transforms as a Lorentz scalar

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 6, 2005, Pages 1-7

  Bender, Carl M ^a   Brandt, Sebastian F ^a   Chen, Jun Hua ^a   Wang, Qinghai ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PARITY; QUANTUM THEORY; SPACE; SPECTRUM; TIME;

EID: 18444379929     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.065010     Document Type: Article

References (22)

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15. It is worthwhile but very difficult to verify that the C operator in (10), as opposed to the C operator in (5), really defines a positive norm for the cubic theory. In the case of the Lee model, the problem with the C operator in (5) is connected with the appearance of degeneracy: It is possible to have two states having the same energy but with different momentum. In the Lee model, only the C operator in (10) gives a physical theory having a positive norm and verifying this can be done explicitly (see Ref. [10]).
16. A way to understand the result in (26) is to observe that adding an imaginary constant to the field ψ, φ ≡ ψ + iεμ-2, replaces the Hamiltonian density in (17) by H new(x,t) = 1/2 π2(x,t) + 1/2μ2φ 2(x,t) + 1/2[∇xφ(x,t)]2 + A, where A is a real constant. Clearly, PI is not a symmetry of the Hamiltonian associated with Hnew because PIφPI = - φ + 2iεμ-2. However, C in (26) is a symmetry of the new Hamiltonian because CφC = -φ.
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