# Questions tagged [complex-numbers]

Numbers of the form $\{z= x+ i\,y:\;x,\, y\in\mathbb{R}\}$ where $i^2 = -1$. Useful especially as quantum mechanics, where system states take complex vector values.

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### Finding complex potential function

Let $\tilde{\chi} = z^{2} -iz + 3$ and use the following theorem to define a new complex potential function $\chi$ such that the unit circle is a streamline: Theorem: Let $\tilde{\chi}$ be a complex ...
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### Can the QFT path integral be re-expressed using a real, positive-definite function of the action? [duplicate]

This question is based on my rather shaky grasp of QFT, so if I'm missing a key concept then just let me know! If you're deriving the Schrodinger equation from the path integral as Feynman did, then ...
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### Connection between Pauli matrices and Quaternions? [duplicate]

reading this sentence from wikipedia: The Pauli matrices (after multiplication by i to make them anti-Hermitian) also generate transformations in the sense of Lie algebras: the matrices iσ1, iσ2, iσ3 ...
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### Reality of Hermitian Operators

I know that Hermitian Operators have all their eigenvalues real. But are the operators themselves real too? So if A is an Hermitian Operator, should it be real, and thus, A = A* be true?
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### Can magnetic Susceptibility be complex?

I have seen that magnetic permeability can be complex at high frequencies. Since there is a lag between $B$ and $H$, their ratio $\mu$ can be complex. If so can the magnetic susceptibility be also ...
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### Hermitian conjugates of Dirac equation

I am given the following Dirac equations: $$(\gamma^{\mu}p_{\mu} - m)u_s(p) = 0\;\;\;\;\;\;\;\;\;eqn\;(1)$$ $$(\gamma^{\mu}p_{\mu} + m)v_s(p) = 0\;\;\;\;\;\;\;\;\;eqn\;(2)$$ where u are the ...
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### What is the fundamental reason for the imaginary unit in Heisenberg's commutator relations?

The well known Heisenberg commutator relation $$[p,q]=\cfrac{\hbar}{i} \cdot \mathbb{I}$$ introduces the imaginary unit $i$ into quantum mechanics. I ask for the deeper reason: Why does the ...
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