Constructive quantum field theory
This article includes a improve this article by introducing more precise citations. (June 2022) ) |
In
Attempts to put quantum field theory on a basis of completely defined concepts have involved most branches of mathematics, including functional analysis, differential equations, probability theory, representation theory, geometry, and topology. It is known that a quantum field is inherently hard to handle using conventional mathematical techniques like explicit estimates. This is because a quantum field has the general nature of an operator-valued distribution, a type of object from mathematical analysis. The existence theorems for quantum fields can be expected to be very difficult to find, if indeed they are possible at all.
One discovery of the theory that can be related in non-technical terms, is that the dimension d of the spacetime involved is crucial. Notable work in the field by James Glimm and Arthur Jaffe showed that with d < 4 many examples can be found. Along with work of their students, coworkers, and others, constructive field theory resulted in a mathematical foundation and exact interpretation to what previously was only a set of recipes, also in the case d < 4.
The traditional basis of constructive quantum field theory is the set of
External links
- Jaffe, Arthur (2000). "Constructive Quantum Field Theory" (PDF). Mathematical Physics 2000: 111–127. ISBN 978-1-86094-230-3.
- Baez, John (1992). Introduction to algebraic and constructive quantum field theory. Princeton, New Jersey: Princeton University Press. OCLC 889252663.