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 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 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 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. 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.

70 pages, actualization, addition of references

References in corpus (12)

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• Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation
• Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research
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• Constructive use of holographic projections
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Cited by in corpus (11)

• Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• A note on Infraparticles and Unparticles
• Localization-Entropy from Holography on Null-Surfaces and the Split Property
• String theory deconstructed
• Indecomposable semiinfinite string-localized positive energy matter and "darkness"
• Poincaré invariant quantum theory, J. Lab lectures
• Constructive use of holographic projections
• Multiple classical limits in relativistic and nonrelativistic quantum mechanics
• Geometry and Localization, a metaphorically related pair
• Soft-Photons and the entanglement of charged qubtis