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mfb- t1_iuhb1j3 wrote

The Dirac equation (1928) is basically the relativistic version of the Schrödinger equation (1925). It still came with the same limits - interactions are not modeled well, you can only look how particles behave in external fields.

QFT is based on special relativity, it wouldn't work without it.

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mumblerfish t1_iuhbpah wrote

Klein-Gordon equation [1] (1926) is also important to mention when it comes to early days of relativistic quantum mechanics.

[1] https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#History

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lagerbaer t1_iuisayz wrote

I'm still amazed by the level of insight, inspiration and daring in going from Klein Gordon to Dirac.

"Hmmm. This naive way of introducing relativity into QM gives us an equation that doesn't appear to describe the electron. What if we made it four-dimension? Oh, and what if we interpret the negative energy solutions as particles, too? And what's this weird behavior of the thing under rotation? Let's call that spin".

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bapt_99 t1_iuixlnh wrote

It's even deeper than that. Dirac noticed that the Klein-Gordon equation didn't produce a positive-definite current density, ρ. There were thus issues with interpreting it as a probability. He postulated a new equation and required that is linear in ∂/∂t, unlike the K-G equation. This would result in the associated continuity equation (the one that would describe the continuous probability) describing an acceptable probability. This immediately lead to other conditions (namely, the equation has to be linear in ∇) due to Lorentz Covariance. He realized his equation had the form of:
i∂ψ/∂t = (-iα•∇+βm)ψ
What are α and β? The hisory goes as "he immediately understood those were 4×4 complex-entries hermitian spinors, with trace 0, determinant and eigenvalues ±1, and that they could be of higher dimension than 4×4 but then this dimension would need to be even"

He no joke deserved his Nobel Prize

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