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Published in:
2019 | OriginalPaper | Chapter
Diffeomorphism Group Representations in Relativistic Quantum Field Theory
Authors : Gerald A. Goldin, David H. Sharp
Published in: Geometric Methods in Physics XXXVI
Publisher: Springer International Publishing
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We explore the role played by the diffeomorphism group and its unitary representations in relativistic quantum field theory. From the quantum kinematics of particles described by representations of the diffeomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar field in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to fields whose quanta are spatially extended objects.