What is the "definition" of a reality constraint and why is it called that way?
(I mean how it is used for example in quantum field theory and string theory)
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A reality constraint typically cuts a quantity with complex degrees of freedom down to the same number of real degrees of freedom. An example of a reality constraint is to impose that a complex $n\times n$ matrix $M\in{\rm Mat_{n\times n}(\mathbb{C})}$ should be Hermitian $M^{\dagger}=M$. A bit more abstractly, one could also call the conditions $M^{\dagger}=-M$ (anti-Hermiticity) and $M^{\dagger}M={\bf 1}_{n\times n}$ (unitarity) for reality conditions, because they also cut the degrees of freedom in half. In quantum theory, one for instance imposes that observables are Hermitian operators and evolution is unitary. |
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