Physics – Quantum Physics
Scientific paper
2006-06-08
Czech.J.Phys.56:999-1006,2006
Physics
Quantum Physics
8 pages, no figures; correction of obvious typos and marginal improvement of formulations
Scientific paper
10.1007/s10582-006-0395-9
A simple derivation of a meaningful, manifestly covariant inner product for real Klein-Gordon (KG) fields with positive semi-definite norm is provided which turns out - assuming a symmetric bilinear form - to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric Quantum Mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.
No associations
LandOfFree
On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-507598