• Corpus ID: 18244000

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}
}
  • B. Schroer
  • Published 16 February 2001
  • Physics, Mathematics
  • arXiv: Mathematical Physics
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… 
View PDF on arXiv
12 Citations
Highly Influential Citations
2
Background Citations
3

12 Citations

Citation Type

Citation Type

Was Von Neumann Right After All
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
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
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
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
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
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
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
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?)
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
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…
...
1
2
...

References

SHOWING 1-10 OF 50 REFERENCES
Local quantum physics : fields, particles, algebras
This textbook gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach, it describes…
The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
The first part of this paper is a review of the author's work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction…
Noncommutative Geometry Year 2000
Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The discovery of quantum mechanics in the form of the noncommuting coordinates on the phase space of atomic…
Form Factors in Completely Integrable Models of Quantum Field Theory
Completely integrable models of quantum field theory the space of physical states the necessary properties of form factors the local commutativity theorem soliton form factors in SG model the…
A mathematical introduction to conformal field theory
Mathematical Preliminaries.- Conformal Transformations and Conformal Killing Fields.- The Conformal Group.- Central Extensions of Groups.- Central Extensions of Lie Algebras and Bargmann's Theorem.-…
Facts and Fictions About Anti deSitter Spacetimes¶with Local Quantum Matter
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
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
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…
Braided Structure in 4-dimensional conformal Quantum Field Theory
Polarization-Free Generators and the S-Matrix
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…
...
1
2
3
4
5
...