- #1

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If it does come up, exactly in what respect?

Thanks!

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- Thread starter "pi"mp
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- #1

- 129

- 1

If it does come up, exactly in what respect?

Thanks!

- #2

Bill_K

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These subjects might have distant uses in physics, depending on the emphasis. I'd suggest asking the instructor if he himself is aware of any physics applications. And if his answer is no, look for another course.

- #3

fzero

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For example, half-integer spins can be understood as so-called projective representations of the rotation group. Furthermore, the possible spins are associated to the fundamental group ##\pi_1(G)## of the Lorentz group. In 3+1 dimensions, this group is ##\pi_1(SO(3,1)=\mathbb{Z}_2## leading to the existence of bosons and fermions. In 2+1 dimensions, one considers ##\pi_1(SO(2,1)=\mathbb{Z}##, which leads to additional representations that are neither fermions nor bosons, called anyons.

A more obvious example which I won't try to over-elaborate on is electromagnetism and more general gauge theories, where the connection between de Rahm cohomology and things like Stokes' theorem are directly relevant. There are additional deep connections between topology and gauge theories. You might browse through Nakahara, Geometry, Topology and Physics for some examples.

Commutative algebra does crop up in some fairly esoteric physics theories. You'd be better off studying as much representation theory of Lie groups/algebras first, since that has applications to almost everything.

- #4

Bill_K

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If you're saying that an understanding of group theory is more important, I agree. If you say that homological algebra will help you understand group theory, I disagree.

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