Quantum field theory (QFT)

Abstract

This chapter outlines (special-relativistic) quantum field theory, with particular emphasis on the roles played therein by time and background dependence. (Fully understanding this chapter rather probably requires having studied at least an elementary course in quantum field theory.) In particular, the current chapter shows that the Wightman axioms for quantum field theory are replete with temporal and background dependent concepts. The Lorentz group, upon which quantum field theory’s equations for each spin of particle rest, is also a background-dependent concept. While there is some interesting contrast with the previous chapter’s account of time in nonrelativistic quantum theory, the main point of this chapter’s exposition is the differences between it and how time is conceived of in general relativity (Chaps. 7 and 8 ). These differences are essential preliminary reading before tackling both Chapter 11’s introduction to Quantum Gravity and Chaps. 9, 10 and 12 ’s introduction to this book’s main topic of the Problem of Time and its Background Independence underpinning. The current chapter also contains this book’s quantum exercises.