Earman, John (2024) Why √-1? The Role of Complex Structure in Quantum Physics. [Preprint]

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Abstract

Standard textbooks on quantum mechanics present the theory in terms of Hilbert spaces over the field of complex numbers and complex linear operator algebras acting on these spaces. What would be lost (or gained) if a different scalar field, e.g. the real numbers or the quaternions, were used? This issue arose with the birthing of the new quantum theory, and over the decades it has been raised over and over again, drawing a variety of different opinions. Here I attempt to identify and to clarify some of the key points of contention, focusing especially on procedures for complexifying real Hilbert spaces and real algebras of observables.

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Item Type:	Preprint
Creators:	Creators Email ORCID Earman, John
Keywords:	quantum physics, real vs. complex Hilbert spaces, complexification, superselection rules
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Realism/Anti-realism General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	John Earman
Date Deposited:	23 Jun 2024 21:07
Last Modified:	23 Jun 2024 21:07
Item ID:	23612
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Realism/Anti-realism General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Date:	22 June 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23612

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