Local Quantum Measurement I Relativistic Consistency, No-Signalling and Local Commutativity

Abstract

Now we come to relativistic quantum theory, but we will not specify a particular quantum theory like \\(N-\\)particle Dirac theory or QED or another QFT. We just assume that quantum mechanical systems are described in the usual way by states \\(\\psi \\) which are vectors in a Hilbert space \\(\\mathcal {H}\\) which carries a unitary representation \\(U{(\\Lambda ,)}\\) of the Poi ncare group \\(\\{\\Lambda ,a\\}\\), where \\(\\Lambda \\) are Lorentz transformations and \\(a\\in \\mathbb {R}^4\\) are space-time translations. During this chapter we will focus on the subgroup of Lorentz boosts, in which case we simply denote the corresponding unitary operators by \\(U(\\Lambda )\\) (where \\(\\Lambda \\) is always only a boost), whereas in the following Chap. 4 we will focus on the space-time translation subgroup and denote the associated unitary operators by U(a).