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In General Relativity the objects transform under the general linear group GL(3,1).

Does this include fermions? If you rotate an object around $360^{\circ}$ the fermions inside the object will not be the same until you rotate it round another $360^{\circ}$.

So what is the generalisation of GL(3,1) to fermions? Is it GL(3,1,C)? or something else? I presume it must have SU(2)xSU(2) as a subgroup.

Vishnu JK
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  • You have to actually define the objects you want to act upon and the type of symmetry you're looking at. It is in general not true that "...In General Relativity the objects transform under the general linear group..." because for example single coordinates transform under diffeomorphisms. Also, "fermions" is very vague: what object do you have in mind? – gented Aug 10 '16 at 17:02
  • Related: http://physics.stackexchange.com/q/225413/2451 and links therein. – Qmechanic Aug 12 '16 at 19:19

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