Pseudoreal quantum fields

We introduce the concept of pseudoreality 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 pseudoreality condition for bosonic fields resolves a longstanding problem with the formulation of gauge theories involving pseudo-Hermitian currents, sheds new light on the resolution of the so-called Hermiticity puzzle, and may allow a consistent minimal coupling of pseudo-Hermitian quantum field theories to gravity. We focus on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>i</a:mi><a:msup><a:mrow><a:mi>ϕ</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msup></a:mrow></a:math> cubic scalar theory, obtaining the relevant pseudoreality conditions up to quadratic order in the coupling; a theory of two complex scalar fields with non-Hermitian mass mixing; and the latter’s coupling to a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>U</c:mi><c:mo stretchy="false">(</c:mo><c:mn>1</c:mn><c:mo stretchy="false">)</c:mo></c:math> gauge field. The general principle of pseudoreality, however, is expected to contribute to the ongoing development of the first-principles construction of pseudo-Hermitian quantum field theories, including their formulation in curved spacetimes.