Question on Olive-Montonen Duality

[metroplex021]

Hi there -- I've just started looking at the topic of dualities in quantum field theory, and I've hit the wall right at the beginning! Looking at the classic Olive-Montonen paper (from 1977), they show how we get elementary quanta of photon, higgs and heavy gauge boson from the Georgi-Glashow model, and that's all familiar and fine. They then say, however, that these correspond to `classical particles' in the limit that h→0, with the charge and quantities in h-bar held fixed in the process. I have two questions about this:

(1) Why do we care about whether or not these quanta correspond to classical particles? Don't we think of particles in terms of field quanta these days?

(2) How can we keep quantities in h-bar fixed given that we're taking the limit in which h→0?

I'm sorry if these seem like stupid or overly specific questions, but since all the literature on duality seems to begin with M-O duality as the simplest example I thought I'd better get this sorted out at the outset! Big thanks to anyone who can help here.

 

[mustang19]

I'll try to give the best response I can.

1) Particles can be a mathematical simplification in some instances, eg during double slit experiments.

2) H bar is a separate constant referring to angular momentum, as long as changes in H do no affect rotation H bar may be defined as a fixed value.

Hope that helps.

 

[metroplex021]

Thanks mustang19 -- that definitely does help. I'm going to re-phrase the first part of my question and ask it again at some point I think, but can I just press you on the latter part about h and h-bar: thank you for your answer because it reassures me that this literature is not completely crazy! I'll keep your answer in mind while I continue to read, but I must say I'm still struggling a bit with how h can be taken to zero and not h-bar, given that the latter is defined in terms of h and 2.pi . Any words or references you could give as to how the latter can be non-zero while the former is taken to zero would be greatly appreciated: but you've already been very helpful so no stress. Thanks again mate.