# [Intuition] Why does the total charge vanish in classical electrodynamics on compact spaces ?

+ 0 like - 0 dislike
67 views

Consider classical electrodynamics on a spacetime of the type $\mathbb{R} \times S$ where $S$ is a 3-dimensional closed manifold. In the article 'K-theory in Quantum Field Theory' (see the statement after equation 3.6), Daniel Freed shows that in such circumstance, the total charge vanishes.

I understand the proof given there, but don't have a Physical intuition for it. Can somebody illuminate this better by providing some intuition ?

Also can this result be taken as an indication that the space slices of our Universe are compact, since we see as much positive charge around as negative charge ? I understand that the total charge *can* vanish even if $S$ is non-compact, but still if we somehow can show that space slices of our universe are compact, we would have an explanation of why the Universe is charge neutral.

Two more related questions :

Does this result hold in quantum field theory too ? And is there an analogous result for non-abelian gauge theories ?

Thanks !

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsO$\varnothing$erflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.