I was trying to make a problem simpler by working in 1+1 spacetime, and I realized that it's far from obvious that quantum physics would even work in this case. Any non-spin related phenomenon could still work (e.g. quantum scalar fields, schrodinger equation) but in less than 2 spatial dimensions angular momentum has no real definition, and in principle shouldn't even be possible. Fermions should be impossible, but no equation comes to mind where I can pinpoint why it breaks down in only 1 spatial dimension (e.g. the Dirac equation still works fine in 1+1).(adsbygoogle = window.adsbygoogle || []).push({});

Another issue I have is the role of Planck's constant throughout all of Quantum physics. This constant isveryclosely related to angular momentum (even though it could just be considered distance*momentum), so in 1+1 dimension is there any quantum phenomenon that still works? Clearly isolated parts of quantum physics, like the schrodinger equation, would not break down on theoretical grounds. However, I'm wondering if something more fundamental such as QFT would fail in the scalar case where Planck's constant will still appear.

I'm a little tired at the moment, but I think what I'm basically looking for an answer to is:

1) Am I correct that no analogue to angular momentum is possible in a 1+1 spacetime?

2) How does the breakdown of angular momentum affect quantum mechanics, given how closely the two are related?

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# Quantum Mechanics in 1+1 spacetime

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