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

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19

Quantum fields on space-time

In this chapter we describe the most important examples of (non-interacting) relativistic quantum fields. We will use extensively the formalism developed in Chap. 18.

Most textbook presentations of this subject start from the discussion of representations of the Poincaré group. They stress that the most fundamental quantum fields are covariant with respect to this group. In our presentation the Poincaré covariance is a secondary property. The property that we emphasize more is the Einstein causality of fields. In the mathematical language this is expressed by the fact that observables belonging to causally separated subsets of space-time commute with one another. This property can be true even when there is no ...

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