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The Conceptual Framework of Quantum Field Theory$
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Anthony Duncan

Print publication date: 2012

Print ISBN-13: 9780199573264

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199573264.001.0001

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Dynamics III: Relativistic quantum mechanics

Dynamics III: Relativistic quantum mechanics

(p.108) 5 Dynamics III: Relativistic quantum mechanics
The Conceptual Framework of Quantum Field Theory

Anthony Duncan

Oxford University Press

This chapter analyzes the implications of the basic underlying symmetry of relativistic quantum field theory: the Poincaré group incorporating the symmetry of such theories under Lorentz transformations and translations in space-time. This is the second of the three fundamental physical ingredients of quantum field theory discussed at length in Chapter 3. Minkowski's introduction in 1908 of a four-dimensional space, in which the Lorentz transformations of special relativity could be interpreted as rotations preserving an indefinite metric, does not expand the physical content of relativity. However, it vastly improves our ability to visualize the physical structure of the theory, and greatly simplifies the search for theories satisfying the constraints of relativistic invariance.

Keywords:   relativistic quantum field theory, Poincaré groups, Lorentz transformations, Minkowski, four-dimensional space

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