# Lectures on Algebraic Quantum Field Theory and Operator Algebras

@article{Schroer2001LecturesOA, title={Lectures on Algebraic Quantum Field Theory and Operator Algebras}, author={Bert Schroer}, journal={arXiv: Mathematical Physics}, year={2001} }

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as "why mathematicians are/should be interested in algebraic quantum field theory" would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical physics with applications in particle and…

## 12 Citations

Was Von Neumann Right After All

- Mathematics
- 2016

The work with TGD inspired model for quantum computation led to the realization that von Neumann algebras, in particular hyper-finite factors of type II1 could provide the mathematics needed to…

MATHEMATICAL ASPECTS OF CONSCIOUSNESS THEORY

- Mathematics
- 2009

This book discusses general mathematical ideas behind TGD inspired theory of consciousness.
PART I: New Physics And Mathematics Involved With TGD
The Clifford algebra associated with point of…

An Overview About Quantum TGD

- Physics
- 2010

This chapter provides a summary about various approaches to quantum TGD. The discussions are based on the general vision that quantum states of the Universe correspond to the modes of classical…

Zero Energy Ontology and Matrices

- Mathematics
- 2019

During years the basic mathematical and conceptual building bricks of quantum TGD have become rather obvious. One important building brick is Zero Energy Ontology (ZEO). ZEO forces to generalize the…

Hyper-Finite Factors, P-Adic Length Scale Hyoithesis, and Dark Matter Hierarchy

- Physics
- 2014

The book is devoted to hyper-finite factors and hierarchy of Planck constants.
Configuration space spinors indeed define a canonical example about hyper-finite factor of type II1. The work with TGD…

Topological Geometrodynamics: Basic Visions

- Physics
- 2010

In this article I will discuss three basic visions about quantum Topological Geometrodynamics (TGD). It is somewhat matter of taste which idea one should call a vision and the selection of these…

Fixed Point Theory Using ψ Contractive Mapping in
C
∗
-Algebra Valued B-Metric Space

- Mathematics
- 2021

In this paper, fixed point theorems using ψ contractive mapping in C∗-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we…

Topological Geometrodynamics : Three Visions

- Physics
- 2010

In this article I will discuss three basic visions about quantum Topological Geometrodynamics (TGD). It is somewhat matter of taste which idea one should call a vision and the selection of these…

Holography&Transplantation and All That (The tip of an iceberg for a paradigmatic change in QFT?)

- Physics
- 2001

Recent developments in local quantum physics have led to revolutionary conceptual changes in the thinking about a more intrinsic formulation and in particular about unexpected aspects of localized…

The Conventionality of Parastatistics

- PhysicsThe British Journal for the Philosophy of Science
- 2015

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles…

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Abstract: It is natural to analyse the AdSd+1-CQFTd correspondence in the context of the conformal-compactification and covering formalism. In this way one obtains additional insight about Rehren's…

Anomalous scale dimensions from time-like braiding

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- 2001

Using previously gained insight about the particle/field relation in conformal quantum field theories, which required interactions to be related to the existence of particle-like states associated…

CHARGED SECTORS, SPIN AND STATISTICS IN QUANTUM FIELD THEORY ON CURVED SPACETIMES

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- 2001

The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a…

Polarization-Free Generators and the S-Matrix

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- 2000

Abstract: Polarization-free generators, i.e. “interacting” Heisenberg operators which are localized in wedge-shaped regions of Minkowski space and generate single particle states from the vacuum, are…