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In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requires new mathematics, in a sense analogous to classical real analysis, putting calculus on a mathematically rigorous foundation.
This line of study is called constructive quantum field theory, a subfield of mathematical physics,: 2 which has led to such results as CPT theorem, spin–statistics theorem, and Goldstone's theorem, and also to mathematically rigorous constructions of many interacting QFTs in two and three spacetime dimensions, e.g. two-dimensional ...
- Haag–Kastler Axioms
- Category-Theoretic Formulation
- QFT in Curved Spacetime
- Further Reading
- External Links
Let O {\displaystyle {\mathcal {O}}} be the set of all open and bounded subsets of Minkowski space. An algebraic quantum field theory is defined via a net { A ( O ) } O ∈ O {\displaystyle \{{\mathcal {A}}(O)\}_{O\in {\mathcal {O}}}} of von Neumann algebras A ( O ) {\displaystyle {\mathcal {A}}(O)} on a common Hilbert space H {\displaystyle {\mathca...
Let Mink be the category of open subsets of Minkowski space M with inclusion maps as morphisms. We are given a covariant functor A {\displaystyle {\mathcal {A}}} from Mink to uC*alg, the category of unital C* algebras, such that every morphism in Mink maps to a monomorphism in uC*alg (isotony). The Poincaré group acts continuously on Mink. There ex...
More recently, the approach has been further implemented to include an algebraic version of quantum field theory in curved spacetime. Indeed, the viewpoint of local quantum physics is in particular suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. Several rigorous results concernin...
Haag, Rudolf; Kastler, Daniel (1964), "An Algebraic Approach to Quantum Field Theory", Journal of Mathematical Physics, 5 (7): 848–861, Bibcode:1964JMP.....5..848H, doi:10.1063/1.1704187, ISSN 0022...Haag, Rudolf (1996) [1992], Local Quantum Physics: Fields, Particles, Algebras, Theoretical and Mathematical Physics (2nd ed.), Berlin, New York: Springer-Verlag, doi:10.1007/978-3-642-61458-3, ISB...Brunetti, Romeo; Fredenhagen, Klaus; Verch, Rainer (2003). "The Generally Covariant Locality Principle – A New Paradigm for Local Quantum Field Theory". Communications in Mathematical Physics. 237...Brunetti, Romeo; Dütsch, Michael; Fredenhagen, Klaus (2009). "Perturbative Algebraic Quantum Field Theory and the Renormalization Groups". Advances in Theoretical and Mathematical Physics. 13 (5):...7 de nov. de 2017 · Constructive quantum field theory is a synthesis of ideas and methods of axiomatic field theory and renormalization theory with modern mathematical methods. The concept of a relativistic quantum field itself admits various equivalent mathematical interpretations, enabling one to use methods from different areas of mathematics.
14 de jul. de 2014 · The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides.
- John C. Baez, Irving Ezra Segal, Zhengfang Zhou
- July 14, 2014
- 1992
the goal of this paper is to provide a perspective on “constructive quantum field theory” (CQFT), the subfield of mathematical physics concerned with establishing the existence of concrete models of relativistic quantum field theory in a very precise mathematical sense and then studying their properties from the point of
4 de out. de 2005 · Constructive Quantum Field Theory. A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
