As these will be essential for an understanding of the quantum black hole system, an outline of this topic is given here.įinally, although we shall not develop a lot of our formalism using the Feynman path-integral technique, we do make use of the basic structure of the path integral in the work on renormalization in chapter 6, and again on interacting fields in curved space in chapter 9. The reader may be unfamiliar with thermal Green functions and metric Euclideanization. Special importance also attaches to Green functions, treated in detail in §2.7. Much of the chapter will be familiar from textbooks such as Bjorken & Drell (1965), but the reader should take special note of the results on the expectation value of the stress–energy–momentum tensor and vacuum divergence (§2.4), as these will play a central role in what follows. This restriction will enable the important features of curved space quantum field theory to emerge with the minimum of mathematical complexity. Most of the detailed analysis will refer to a scalar field, but the main results will be listed for higher spins also.
![tensor field curved space tensor field curved space](https://steamcdn-a.akamaihd.net/steam/apps/1320230/ss_81251db7a8be2e544132dfc3b16210a29bd1a14c.1920x1080.jpg)
In the later chapters we shall follow the treatment given here. A great deal of the formalism can be extended to curved spacetime and non-trivial topologies with little or no modification.
![tensor field curved space tensor field curved space](http://i.stack.imgur.com/4LdVY.gif)
Isotropic distributions are more frequent and pronounced in proximity of the corners distant to the inlet. In the near field of the inlet a trend towards anisotropy with principle directions perpendicular to local velocity vectors can be observed. In this chapter we shall summarize the essential features of ordinary Minkowski space quantum field theory, with which we assume the reader has a working knowledge. The represented tensor-valued field shows strong inhomogeneities across the solution domain.