Quote from Feynman and Hibbs book

[exmarine]

Page 260: "No modification of quantum electrodynamics at high frequencies is known which simultaneously makes all result finite, maintains relativistic invariance, and keeps the sum of probabilities over all alternatives equal to unity."

Is that still true today?

 

[Demystifier]

The standard way to avoid these problems is to apply the renormalization theory to quantum electrodynamics. However, the issue of "finiteness" is somewhat tricky. The final measurable results are finite, but they are obtained by a somewhat dirty method of subtraction of infinite quantities.

On the other hand, string theory can be counted as a "really finite" counterexample, but it is dubious to which extent it can be considered to be a "modification" of quantum electrodynamics.

 

[bhobba]

What's going on in renormalisation is much better understood today.

Check out:
http://arxiv.org/pdf/hep-th/0212049.pdf

I wouldn't describe as the subtraction of infinite quantities - I would describe it as a trick to change a lousy perturbation parameter. In perturbation theory one normally chooses a parameter to perturb about that is small. The coupling constant looked a good choice because it was small but in fact it turned out to be really lousy being - wait for it - infinity - gulp. Of course its a blemish a theory has sensible quantities like coupling constants that are infinite. The modern resolution is to say the theory is only valid up to some cut-off. But what cut-off? That's where renormalisable theories are nice - it turns out that quantities you can actually measure don't depend on that cut-off - quantities that are infinite without the cut-off do - but one can figure out what they should be for a specific cut-off based on measurement. In fact that's all renormalised parameters are - simply a value found by experiment that we know must be true and will not be cut-off dependent - they can be safely relied on to perturb about. A fancy name for what is in fact a simple idea - once you get used to it

Thanks
Bill