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Danu
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I think because the wavefunctions are required to be normalized so that $\psi^{\dagger}\psi$$\psi^{*}\psi$ represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

I think because the wavefunctions are required to be normalized so that $\psi^{\dagger}\psi$ represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

I think because the wavefunctions are required to be normalized so that $\psi^{*}\psi$ represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

I think because the wavefunctions are required to be normalized so that ΨΨ*$\psi^{\dagger}\psi$ represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

I think because the wavefunctions are required to be normalized so that ΨΨ* represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

I think because the wavefunctions are required to be normalized so that $\psi^{\dagger}\psi$ represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.

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I think because the wavefunctions are required to be normalized so that ΨΨ* represents the probability or probability density of finding the particle, so their amplitude are not allowed to scale arbitrarily. That's why the gauge field can only be real.