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

3

Tensor algebras

In this chapter we study various constructions related to the tensor product of vector spaces. In particular, we introduce symmetric and anti-symmetric tensor algebras, whose Hilbert space versions are called bosonic and fermionic Fock spaces. Fock spaces are fundamental tools used to describe quantum field theories in terms of particles.

We also discuss the notions of determinants, volume forms and Pfaffians, which are closely related to anti-symmetric tensors.

3.1 Direct sums and tensor products

There are several non-equivalent versions of the tensor product of two infinite-dimensional vector spaces. We will introduce two of them, which are especially useful: the algebraic tensor product and the tensor product in the sense ...

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