- Axiomatic quantum field theory
- Algebraic quantum field theory
- Quantum field theory
- Wightman axioms
- Constructive quantum field theory
- Arthur Wightman
- Quantum field theory in curved spacetime
- Edge-of-the-wedge theorem
- Gelfand–Naimark–Segal construction
- Schwinger function
Kingdom of Heaven (2005)
Avengers: Infinity War (2018)
Signs (2002)
The Outpost (2020)
Gladiator (2000)
Jean de Florette (1986)
Axiomatic quantum field theory GudangMovies21 Rebahinxxi LK21
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective.
There are two main challenges in this discipline. First, one must propose a set of axioms which describe the general properties of any mathematical object that deserves to be called a "quantum field theory". Then, one gives rigorous mathematical constructions of examples satisfying these axioms.
Analytic approaches
= Wightman axioms
=The first set of axioms for quantum field theories, known as the Wightman axioms, were proposed by Arthur Wightman in the early 1950s. These axioms attempt to describe QFTs on flat Minkowski spacetime by regarding quantum fields as operator-valued distributions acting on a Hilbert space. In practice, one often uses the Wightman reconstruction theorem, which guarantees that the operator-valued distributions and the Hilbert space can be recovered from the collection of correlation functions.
= Osterwalder–Schrader axioms
=The correlation functions of a QFT satisfying the Wightman axioms often can be analytically continued from Lorentz signature to Euclidean signature. (Crudely, one replaces the time variable
t
{\displaystyle \;t\;}
with imaginary time
τ
=
−
−
1
t
;
{\displaystyle \;\tau =-{\sqrt {-1\,}}\,t~;}
the factors of
−
1
{\displaystyle \;{\sqrt {-1\,}}\;}
change the sign of the time-time components of the metric tensor.) The resulting functions are called Schwinger functions. For the Schwinger functions there is a list of conditions — analyticity, permutation symmetry, Euclidean covariance, and reflection positivity — which a set of functions defined on various powers of Euclidean space-time must satisfy in order to be the analytic continuation of the set of correlation functions of a QFT satisfying the Wightman axioms.
= Haag–Kastler axioms
=The Haag–Kastler axioms axiomatize QFT in terms of nets of algebras.
= Euclidean CFT axioms
=These axioms (see e.g.) are used in the conformal bootstrap approach to conformal field theory in
R
d
{\displaystyle \mathbb {R} ^{d}}
. They are also referred to as Euclidean bootstrap axioms.
See also
Dirac–von Neumann axioms
References
Streater, R. F.; Wightman, A. S. (1964). PCT, Spin and Statistics, and All That. New York: W. A. Benjamin. OCLC 930068.
Bogoliubov, N.; Logunov, A.; Todorov, I. (1975). Introduction to Axiomatic Quantum Field Theory. Reading, Massachusetts: W. A. Benjamin. OCLC 1527225.
Araki, H. (1999). Mathematical Theory of Quantum Fields. Oxford University Press. ISBN 0-19-851773-4.
Kata Kunci Pencarian:
Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway ...
Introduction to Axiomatic Quantum Field Theory (Mathematical Physics ...
Perturbative Quantum Electrodynamics and Axiomatic Field Theory von ...
Quantum Field Theory, as Simply as Possible | Princeton University Press
(PDF) Review: N. N. Bogolubov, A. A. Logunov and I. T. Todorov ...
Quantum Field Theory and Chaos Explains Everything | HubPages
(PDF) Current Trends in Axiomatic Quantum Field Theory
Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway ...
(PDF) Axiomatic Quantum Field Theory in Terms of Operator Product ...
Quantum Field Theory, as Simply as Possible | Princeton University Press
Abstract Quantum Field Theory Digital Art by GeoPattern - Fine Art America
دانلود کتاب Introduction to Axiomatic Quantum Field Theory - بلیان