Localization and the interface between quantum mechanics, quantum field theory and quantum gravity
Abstract
We show that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Bornlocalization in QM (which in the relativistic context changes its name to NewtonWigner localization) and modular localization which is the localization underlying QFT, after one liberates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The BornNewtonWigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. Taking these significant differences serious has not only repercussions for the philosophy of science, but also leads to a new structural properties as a consequence of vacuum polarization: the area law for localization entropy near the the causal localization horizon and a more realistic cutoff independent setting for the cosmological vacuum energy density which is compatible with local covariance. The article presents some observations about the interface between QFT in CST and QG.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.4600
 Bibcode:
 2007arXiv0711.4600S
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Nuclear Theory;
 Quantum Physics
 EPrint:
 70 pages, actualization, addition of references