Chapter

Dynamics IV: Aspects of locality: clustering, microcausality, and analyticity

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print August 2012 | ISBN: 9780199573264
Published online January 2013 | e-ISBN: 9780191743313 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199573264.003.0006
Dynamics IV: Aspects of locality: clustering, microcausality, and analyticity

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Chapter 5 discussed two possible approaches to constructing a relativistically invariant theory of particle scattering. The first attempt — a frontal assault in which one directly writes down for each scattering sector (i.e., with a specified number of incoming and outgoing particles) a manifestly Lorentz-invariant interaction operator containing momentum-dependent Lorentz scalar amplitudes — led to disaster. The resultant theory led to particle interactions which could not be confined to finite regions of space-time. The second attempt, in which the interaction Hamiltonian is written as a spatial integral of a local, Lorentz (ultra-)scalar field, accomplishes the primary goal of producing a Lorentz-invariant set of scattering amplitudes, but its compliance with the clustering principle remains uncertain. This chapter puts this latter requirement into a precise mathematical framework, called second quantization, so that the process of identifying clustering relativistic scattering theories can be simplified and even to some degree automated.

Keywords: relativistic quantum field theory; particle scattering; Hamiltonians; Lorentz transformations; clustering principle; second quantization

Chapter.  20613 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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