… but there is a very intuitive simple way to understand the beta function. This was worked out by N.K. Nielsen and Richard Hughes way back in the 70’s. In the presence of an external background magnetic field, Landau diamagnetism gives a positive contribution. But the spin of the gluon gives a contribution from Pauli paramagnetism, of the opposite sign, which is also larger by a factor of 12, resulting in an overall coefficient of -11.
Not to say Costello’s method has no value, but I think it requires more sophistication than the old explanation above.
Peter Orland, Yes, thanks, that is a good physical way of understanding the result of the calculation.
Costello is providing not a new physical interpretation like this, but a new mathematical interpretation. What’s very unusual here is that we’re seeing a new and very non-trivial mathematical interpretation not of some random aspect of some random quantum field theory, but of a central aspect of a central part of the Standard Model. Such a thing doesn’t come along very often…
… but there is a very intuitive simple way to understand the beta function. This was worked out by N.K. Nielsen and Richard Hughes way back in the 70’s. In the presence of an external background magnetic field, Landau diamagnetism gives a positive contribution. But the spin of the gluon gives a contribution from Pauli paramagnetism, of the opposite sign, which is also larger by a factor of 12, resulting in an overall coefficient of -11.
Not to say Costello’s method has no value, but I think it requires more sophistication than the old explanation above.
Peter Orland,
Yes, thanks, that is a good physical way of understanding the result of the calculation.
Costello is providing not a new physical interpretation like this, but a new mathematical interpretation. What’s very unusual here is that we’re seeing a new and very non-trivial mathematical interpretation not of some random aspect of some random quantum field theory, but of a central aspect of a central part of the Standard Model. Such a thing doesn’t come along very often…