Open AccessComplex Covariance
Author(s) -
Frieder Kleefeld
Publication year - 2013
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/1809
Subject(s) - general covariance , hermitian matrix , phase space , classical limit , theory of relativity , physics , classical mechanics , lorentz transformation , correspondence principle (sociology) , degrees of freedom (physics and chemistry) , lorentz covariance , dirac (video compression format) , covariance , theoretical physics , mathematical physics , mathematics , general relativity , quantum mechanics , quantum , epistemology , philosophy , statistics , neutrino
According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory.