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Does quantum field theory exist? Final Lecture, Mathematics 189, Spring 1998
 

Summary: Does quantum field theory exist?
Final Lecture, Mathematics 189, Spring 1998
W. Arveson
We have seen how to quantize a finite dimensional classical mechanical system
(this will be reveiwed briefly below). The purpose of this lecture is to formulate a
mathematical problem associated with the quantization of interacting Boson fields,
to describe the serious mathematical problems assiciated with finding a (mathe-
matically sound) solution to the problem, and to make some remarks about the
nature of the difficulties. The problem remains unsolved to this day.
Consider a nonlinear wave equation in four spacetime dimensions of the form
(1) + + 3
= 0.
Here, = (t, x, y, z) is a function defined on RR3
, and are positive constants,
and is the wave operator
=
2

t2
- =

  

Source: Arveson, William - Department of Mathematics, University of California at Berkeley

 

Collections: Mathematics