Are Rindler quanta real? Inequivalent particle concepts in quantum field theory

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the `reality' of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e. inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a `particle' will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the very same region of spacetime. We shall defend the idea that these representations provide complementary descriptions of the same state of the field against the claim that they embody completely incommensurable theories of the field. 1 Introduction 2 Inequivalent field quantizations 2.1 The Weyl algebra 2.2 Equivalence and disjointness of representations 2.3 Physical equivalence of representations 3 Constructing representations 3.1 First quantization (`splitting the frequencies') 3.2 Second quantization (Fock space) 3.3 Disjointness of the Minkowski and Rindler representations 4 Minkowski versus Rindler quanta 4.1 The paradox of the observer-dependence of particles 4.2 Minkowski probabilities for Rindler number operators 4.3 Incommensurable or complementary? 5 Conclusion Appendix.