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

Abstract

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. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. Both parts together form a rather comprehensive presentation of known consequences of the two antagonistic localization concepts, including the those of its misunderstandings in string theory.

63 pages corrections, reformulations, references added

References in corpus (6)

• Entanglement, Haag-duality and type properties of infinite quantum spin chains
• Particle Weights and their Disintegration II
• Unexplored regions in QFT and the conceptual foundations of the Standard Model
• A note on Infraparticles and Unparticles
• Equivalent Hamiltonians
• Conformal quantum field theory in various dimensions

Cited by in corpus (12)

• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Positivity and causal localizability in higher spin quantum field theories
• Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy
• The Ongoing Impact of Modular Localization on Particle Theory
• Causality and dispersion relations and the role of the S-matrix in the ongoing research
• The foundational origin of integrability in quantum field theory
• Pascual Jordan's legacy and the ongoing research in quantum field theory
• Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG)
• Interactions with quadratic dependence on string-localized massive vectormesons: massive scalar quantum electrodynamics
• The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics
• Placing hidden properties of quantum field theory into the forefront: wedge localization and a new constructive on-shell setting
• Emergent Gauge Symmetries and Quantum Operations