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Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason asthat the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next? How to prove from this, that there can be arbitrary phase generated on exchange? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason as the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next? How to prove from this, that there can be arbitrary phase generated on exchange? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason that the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next? How to prove from this, that there can be arbitrary phase generated on exchange? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

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# anyons Anyons only in two2+1 spacetime dimensions - better explanation

Regrading why anyonsanyons exist only in two 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason as the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next  ? How to prove from this, that there can be arbitrary phase generated on exchange  ? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

# anyons only in two dimensions - better explanation

Regrading why anyons exist only in two dimensions (which have an arbitrary phase on exchange), I read the reason as the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next  ? How to prove from this, that there can be arbitrary phase generated on exchange  ? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

# Anyons only in 2+1 spacetime dimensions - better explanation

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason as the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next? How to prove from this, that there can be arbitrary phase generated on exchange? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.

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# anyons only in two dimensions - better explanation

Regrading why anyons exist only in two dimensions (which have an arbitrary phase on exchange), I read the reason as the paths for exchange in 3D are deformable into each other while in 2D, they may not be deformed into each other. So what is next ? How to prove from this, that there can be arbitrary phase generated on exchange ? I understand that in 2D, we have braids, but can I get a proof for an arbitrary phase on exchange which specifically takes into account the topological equivalence of paths in 3D and not in 2D.