Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)

Understand

It is shown 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 distiction between Born-localization in QM (which in the relativistic context changes its name to Newton-Wigner localization) and modular localization which is the localization underlying QFT, after one separates 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 Born-Newton-Wigner 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.