Pseudo-real quantum fields

• URL: http://arxiv.org/abs/2501.09111v1
• Date: Wed, 15 Jan 2025 19:46:16 GMT
• Title: Pseudo-real quantum fields
• Authors: Maxim N. Chernodub, Peter Millington, Esra Sablevice,
• Abstract summary: We show that the concept of pseudo-reality for complex numbers provides a unifying framework for two approaches to quantum field theories. The pseudo-reality condition for bosonic fields resolves a long-standing problem with the formulation of gauge theories involving pseudo-Hermitian currents. Results contribute significantly to the ongoing development of the first-principles construction of pseudo-Hermitian quantum field theories.
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• Abstract: We introduce the concept of pseudo-reality for complex numbers. We show that this concept, applied to quantum fields, provides a unifying framework for two distinct approaches to pseudo-Hermitian quantum field theories. The first approach stems from analytically continuing Hermitian theories into the complex plane, while the second is based on constructing them from first principles. The pseudo-reality condition for bosonic fields resolves a long-standing problem with the formulation of gauge theories involving pseudo-Hermitian currents, sheds new light on the resolution of the so-called Hermiticity Puzzle, and leads to a consistent minimal coupling of pseudo-Hermitian quantum field theories to gravity. These results contribute significantly to the ongoing development of the first-principles construction of pseudo-Hermitian quantum field theories, including their formulation in curved spacetimes.

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