scholarly journals Localization in quantum field theory

2017 ◽  
Vol 14 (08) ◽  
pp. 1740008 ◽  
Author(s):  
A. P. Balachandran
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Black Hole Physics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Unruh Effect ◽  
Quantum Field ◽  
Simple Derivation ◽  
Spatial Region

In non-relativistic quantum mechanics, Born’s principle of localization is as follows: For a single particle, if a wave function [Formula: see text] vanishes outside a spatial region [Formula: see text], it is said to be localized in [Formula: see text]. In particular, if a spatial region [Formula: see text] is disjoint from [Formula: see text], a wave function [Formula: see text] localized in [Formula: see text] is orthogonal to [Formula: see text]. Such a principle of localization does not exist compatibly with relativity and causality in quantum field theory (QFT) (Newton and Wigner) or interacting point particles (Currie, Jordan and Sudarshan). It is replaced by symplectic localization of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localization gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with “continuous” spin. This review outlines the basic principles underlying symplectic localization and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.

scholarly journals The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1324
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Superposition Principle ◽  
Hamiltonian Formalism ◽  
Scalar Fields ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Entropic Dynamics

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

scholarly journals Test of the Hypothesis of Realism Using a Modified Version of Wigner Inequality

2019 ◽  
Vol 222 ◽  
pp. 03003
Author(s):  
Nikolay Nikitin ◽  
Konstantin Toms
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Current Work ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Pseudoscalar Mesons

In the current work we present a modified Wigner inequality for test of the hypothesis of realism. This modified Wigner inequality is suitable for test of realism not only in systems that obey the laws of non-relativistic quantum mechanics, but also in systems that obey the laws of quantum field theory. We show how this inequality can be violated in systems of neutral pseudoscalar mesons.

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