The Field $\mathbb{F}$ of A Hilbert Space

Asked Aug 22 '18 at 09:53

Active Aug 22 '18 at 15:10

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Is it always necessary for the field of some arbitrary Hilbert space I define to describe a system be a field of complex numbers only? Is it possible to have a field of naturals, or reals?

Since the vectors in the Hilbert space can be whatever I want (if I follow the two-three rules), I was wondering if the definition is agnostic to the elements in the field as well.

edited Aug 22 '18 at 15:10

Qmechanic

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asked Aug 22 '18 at 09:53

Mahathi Vempati

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The naturals isn't a field. As for the why not reals, I suggest reading this https://physics.stackexchange.com/q/32422/ as it has already been asked there. – Gold Aug 22 '18 at 10:47
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Possible duplicate of QM without complex numbers – stafusa Aug 22 '18 at 13:04

The Field $\mathbb{F}$ of A Hilbert Space

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