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The Aharonov-Bohm effect for nonAbelian gauge fields is subtle, even the definition of flux and charge is more complicated thenthan Abelian cases. Both charge and flux can be nonAbelian. A flux is defined as a conjugation class of the gauge group G, and a charge is a (irreducible) representation of (subgroup of) the gauge group.

However, (in 2D) a general particle may carry both flux and charge. For given gauge group, there are fixed number of elementary particles, they are classified by so called supersecltion sectors.

Suppose a charged particle C carries a nontrivial flux which is non commuting with another flux F, when C moves around F, both C and F will be transformed by a group action. For this reason, there will be no AB effect (or no interference) in this case since we can tell which way the particle C comes to the screen by measuring its flux (different ways result in different flux). Non trivial AB effect can be oberved only when the flux carried by C commutes with F.

For reference, see Preskill's lecture notes about topological quantum computation, it is friendly for beginers (like me):

http://www.theory.caltech.edu/~preskill/ph219/topological.pdf

The Aharonov-Bohm effect for nonAbelian gauge fields is subtle, even the definition of flux and charge is more complicated then Abelian cases. Both charge and flux can be nonAbelian. A flux is defined as a conjugation class of the gauge group G, and a charge is a (irreducible) representation of (subgroup of) the gauge group.

However, (in 2D) a general particle may carry both flux and charge. For given gauge group, there are fixed number of elementary particles, they are classified by so called supersecltion sectors.

Suppose a charged particle C carries a nontrivial flux which is non commuting with another flux F, when C moves around F, both C and F will be transformed by a group action. For this reason, there will be no AB effect (or no interference) in this case since we can tell which way the particle C comes to the screen by measuring its flux (different ways result in different flux). Non trivial AB effect can be oberved only when the flux carried by C commutes with F.

For reference, see Preskill's lecture notes about topological quantum computation, it is friendly for beginers (like me):

http://www.theory.caltech.edu/~preskill/ph219/topological.pdf

The Aharonov-Bohm effect for nonAbelian gauge fields is subtle, even the definition of flux and charge is more complicated than Abelian cases. Both charge and flux can be nonAbelian. A flux is defined as a conjugation class of the gauge group G, and a charge is a (irreducible) representation of (subgroup of) the gauge group.

However, (in 2D) a general particle may carry both flux and charge. For given gauge group, there are fixed number of elementary particles, they are classified by so called supersecltion sectors.

Suppose a charged particle C carries a nontrivial flux which is non commuting with another flux F, when C moves around F, both C and F will be transformed by a group action. For this reason, there will be no AB effect (or no interference) in this case since we can tell which way the particle C comes to the screen by measuring its flux (different ways result in different flux). Non trivial AB effect can be oberved only when the flux carried by C commutes with F.

For reference, see Preskill's lecture notes about topological quantum computation, it is friendly for beginers (like me):

http://www.theory.caltech.edu/~preskill/ph219/topological.pdf

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source | link

The Aharonov-Bohm effect for nonAbelian gauge fields is subtle, even the definition of flux and charge is more complicated then Abelian cases. Both charge and flux can be nonAbelian. A flux is defined as a conjugation class of the gauge group G, and a charge is a (irreducible) representation of (subgroup of) the gauge group.

However, (in 2D) a general particle may carry both flux and charge. For given gauge group, there are fixed number of elementary particles, they are classified by so called supersecltion sectors.

Suppose a charged particle C carries a nontrivial flux which is non commuting with another flux F, when C moves around F, both C and F will be transformed by a group action. For this reason, there will be no AB effect (or no interference) in this case since we can tell which way the particle C comes to the screen by measuring its flux (different ways result in different flux). Non trivial AB effect can be oberved only when the flux carried by C commutes with F.

For reference, see Preskill's lecture notes about topological quantum computation, it is friendly for beginers (like me):

http://www.theory.caltech.edu/~preskill/ph219/topological.pdf