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2 votes
Accepted

Closed form expression of 2D CFT integral

We identify OP's complex plane $\mathbb{C}\cong\mathbb{R}^2$ with a $d=2$ real plane. Let us for fun generalize to $d$ spacetime dimensions. Let the total conformal weight be $\Delta:=\Delta_1+\...
Qmechanic's user avatar
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2 votes

If quaternions are an extension of complex numbers, is there a study of EM wave theory in terms of quaternions?

There is a generalisation, but it uses the next level up from the quaternions. There is a type of algebra with a strong geometric interpretation called a Clifford algebra. It can be thought of as a ...
Nullius in Verba's user avatar
1 vote
Accepted

Equation for real/complex $\phi^4$ theory

For what it is worth, the standard convention is to divide each term in the Lagrangian with its symmetry factor, e.g. $${\cal L}~=~\mp \frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^2\...
Qmechanic's user avatar
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1 vote

Is the scalar field in the Yukawa interaction real or complex?

The current $\bar\psi \gamma^\mu \psi$ will be equal to zero if $\psi$ is a Majorana fermion. This condition is the fermion analogue of being "real."
mike stone's user avatar
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1 vote
Accepted

Lorentz Boosts and Hyperbolic Quaternions

I'd never heard of hyperbolic quaternions, and they seem very strange – not even an alternative algebra, which is worse than the octonions. The subspace $a+br$ is isomorphic to the split-complex ...
benrg's user avatar
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1 vote
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Intensity and complex electric field

First thing to notice is that the Poynting Vector is "redefine" when dealing with complex functions. This is something usually overlooked by books, Jackson's for exemple doesn't even bother ...
koy's user avatar
  • 134

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