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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

The definition of local observables in quantum field theory

ANTON Z. CAPRI

Published Sep 1, 1969• 1 citation
Publisher
DOI
10.1007/bf02711057

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There have been many discussions about whether all observational propositions in nonrelativistic quantum mechanics can be taken as simultaneously definite without contradiction. Von Neumann, Jauch and Piron, and Bell have shown that not all observational propositions in nonrelativistic quantum mechanics can be interpreted in this way. In the present paper, I examine these theorems from an operator algebraic point view in order to apply these theorems to algebraic quantum field theory. Then I point out that not all observational propositions in local algebras can be taken as definite, in addition to nonrelativistic quantum mechanics.
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantum symmetries and algebras of field operators. For every algebra A of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field operators are obtained which act on a positive definite Hilbert space of states and transform covariantly under the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation relations, these fields are demonstrated to obey local braid relation. Contents 1 Introduction 1 2 The Notion of Quantum Symmetry 5 3 Algebraic Methods for Field Construction 9 3.1 Observables and superselection sectors in local quantum field theory . . . . 10 3.2 Localized endomorphisms and fusion structure . . . . . ....
This paper provides a self-consistent explanation of Schrödinger's Cat paradox within the framework of Time Field Theory (TFT). Starting from the axioms of conservation of local intrinsic total speed and spacetime flux conservation, TFT derives the core proposition: Mass as Observer. A massive entity carries its own local time benchmark and possesses the definitional power of physical quantities, while the wavefunction serves only as a background probability description without definitional power. In the Schrödinger’s Cat setup, the cat, Geiger counter, and poison bottle are natural observers; once the radioactive atom couples to the counter, its state is locked to a definite value, so the cat’s life or death is determined before the box is opened. The paradox arises from inverted definitional priority: using a massless background to describe a massive observer. TFT unifies the description of gravity and quantum measurement within flat Euclidean space, without introducing consciousness, parallel worlds, or hidden variables.