O'Reilly logo

Mathematics of Quantization and Quantum Fields by Christian Gérard, Jan Derezinski

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

4

Analysis in L2 (d)

In this chapter we describe basic properties of operators acting on L2(d). After a preliminary Sect. 4.1, we will study the Weyl commutation relations and prove the famous Stone–von Neumann uniqueness theorem. Then we define the so-called x, D-quantization, with position to the left and the momentum to the right. We will compare it to the D, x-quantization, which uses the reverse order of position and momentum. The Weyl–Wigner quantization, in some sense superior to the x, D- and D, x-quantizations, will be introduced in

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required