Relativistic Quantum Mechanics and Field Theory
F. Strocchi
TL;DR
This paper reviews the foundational issues in relativistic quantum mechanics and quantum field theory, focusing on conflicts between Hilbert space structure, locality, and gauge invariance.
Contribution
It critically examines the problems and conflicts in relativistic quantum mechanics and their implications for the foundations of quantum field theory.
Findings
Identifies conflicts between Hilbert space and locality
Discusses gauge invariance and Gauss' law issues
Analyzes different quantization approaches for gauge fields
Abstract
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields
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