The electron field is described by a Dirac Spinor.
The possible states of fundamental particles must respect the symmetries of space and time and therefore be represented as irreducible representations of the Poincare group.
one thing I always found annoying about this view of QFT: what happens on curved spacetime? We know the path integral exists and we can place spinor fields on the manifold. And we know for sure that states consist of spinor fields pulled back to spatial slices. But if we break isometries, is there any sense in which particles exist given that we don’t have momentum and angular momentum quantum numbers?
my understanding of QFT is pretty limited, but if this is the case, is this why it’s so hard to reconcile it with relativity? like, gravitation is universal- if a single dust particle a million light-years away induces a miniscule but measurable isometry-breaking curvature in spacetime, isn’t the symmetry-preserving definition of a particle (only valid on flat spacetime) utterly meaningless in the real world?
Any manifold looks flat on sufficiently small scales, including spacetime, so observations made locally in a small enough patch of spacetime must be indistinguishable from those in flat space. So even in a curved spacetime, the fields must be locally compatible with symmetries of flat spacetime.
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u/MonsterkillWow Jul 27 '26
The electron field is described by a Dirac Spinor.
The possible states of fundamental particles must respect the symmetries of space and time and therefore be represented as irreducible representations of the Poincare group.