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This is a follow-up on thisthis answer, where ACuriousMind wrote

Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, respectively.

I understand the basics of representation theory, and I know the $U(1)$ gauge transformations of the QED Lagrangian (I suppose that's the connection between electric charge and the circle group $U(1)$). I also have seen the basics of non-abelian gauge transformations.

However, I wasn't aware that there is a connection between representation theory and the conserved electric charge. Moreover, I had no idea that mass had anything to do with irreps of the Poincaré group.

What are the details of that connection? Why do mass and charge classify irreps?

This is a follow-up on this answer, where ACuriousMind wrote

Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, respectively.

I understand the basics of representation theory, and I know the $U(1)$ gauge transformations of the QED Lagrangian (I suppose that's the connection between electric charge and the circle group $U(1)$). I also have seen the basics of non-abelian gauge transformations.

However, I wasn't aware that there is a connection between representation theory and the conserved electric charge. Moreover, I had no idea that mass had anything to do with irreps of the Poincaré group.

What are the details of that connection? Why do mass and charge classify irreps?

This is a follow-up on this answer, where ACuriousMind wrote

Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, respectively.

I understand the basics of representation theory, and I know the $U(1)$ gauge transformations of the QED Lagrangian (I suppose that's the connection between electric charge and the circle group $U(1)$). I also have seen the basics of non-abelian gauge transformations.

However, I wasn't aware that there is a connection between representation theory and the conserved electric charge. Moreover, I had no idea that mass had anything to do with irreps of the Poincaré group.

What are the details of that connection? Why do mass and charge classify irreps?

1
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What's the relation between representation theory and mass / electric charge?

This is a follow-up on this answer, where ACuriousMind wrote

Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, respectively.

I understand the basics of representation theory, and I know the $U(1)$ gauge transformations of the QED Lagrangian (I suppose that's the connection between electric charge and the circle group $U(1)$). I also have seen the basics of non-abelian gauge transformations.

However, I wasn't aware that there is a connection between representation theory and the conserved electric charge. Moreover, I had no idea that mass had anything to do with irreps of the Poincaré group.

What are the details of that connection? Why do mass and charge classify irreps?