Contributions in Mathematical Physics pp 123-146 | Cite as

# Where’s That Quantum?

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## Abstract

Quantum field theory is the study of quantum systems with an infinite number of degrees of freedom. The simplest quantum field theories are the free bose fields, which are essentially assemblies of an infinite number of coupled oscillators. Examples include the quantized electromagnetic field, lattice vibrations in solid state physics, and the Klein-Gordon field, some of which are relativistic while others are not. Particles show up in quantum field theory as “field quanta.” As we will see, these do not quite have all the properties of the usual particles of Newtonian physics or of Schrödinger quantum mechanics. I will in particular show (Section 3) that the quanta of free bose fields, relativistic or not, can not be perfectly localized in a bounded subset of space. This, in my opinion, shows conclusively that the difficulties encountered when attempting to define a position observable for the field quanta of relativistic fields, that continue to be the source of regular debate in the literature [20] [21] [22] [3] [10] [15] [18] [19] [48] [47], do not find their origin in any form of causality violation, as seems to be generally thought. Instead, they result from an understandable but ill-fated attempt to force too stringent a particle interpretation on the states of the quantum field containing a finite number of quanta.

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