3 ms·

Lattice QCD codes may have what you’re looking for. Having said that, I went down that rabbit hole a few years back and found only impenetrable numeric code wit

Lattice QCD codes may have what you’re looking for. Having said that, I went down that rabbit hole a few years back and found only impenetrable numeric code with little explanation of where the formulas came from. Worse still, practically all such “codes” use shortcuts, simplifications, or outright non-physical spacetimes to reduce the computer power required. You and I are looking for the same thing, so if you do find a good reference please reply!

colanderman 2y ago
Thanks for the lead! That definitely sounds like the direction I'm looking in.
l33tman 2y ago
Lattice QCD is a rabbit hole (like all other advanced subjects) but it's IMO a somewhat conceptually more accessible rabbit hole than the canonical QFT formalism with the Feynman diagrams and perturbation theory. LQCD is built around a "clean" approach that is at least possible to visualize - you go back to the basics, which is that you need to do a sum over every possible combination of field configurations (as this is what it seems the universe does). This is obviously intractable even for a small array, but the concept is easy and the QCD sector of the SM is very clean in interactions. The sum is intractable not because it's big but because it can't be sanely approximated by lesser sums, due to the nature of what you're summing - an exponent of i * the integral of the Lagrangian over each spacetime field configuration. This vary likes crazy so if you skip the some parts you might get a completely different result. The trick to anyhow get anything out of this is to restrict yourself to observables that can be calculated from the ground state, which turn out to be accessible by doing the field integrals over imaginary time instead. This is a trick of calculus, it's not really "non-physical", although it is a pretty crazy method :) This has allowed practitioners to calculate hadron masses for example, it's getting better and better over the decades.

colanderman 2y ago

Thanks for the lead! That definitely sounds like the direction I'm looking in.

l33tman 2y ago

Lattice QCD is a rabbit hole (like all other advanced subjects) but it's IMO a somewhat conceptually more accessible rabbit hole than the canonical QFT formalism with the Feynman diagrams and perturbation theory. LQCD is built around a "clean" approach that is at least possible to visualize - you go back to the basics, which is that you need to do a sum over every possible combination of field configurations (as this is what it seems the universe does). This is obviously intractable even for a small array, but the concept is easy and the QCD sector of the SM is very clean in interactions. The sum is intractable not because it's big but because it can't be sanely approximated by lesser sums, due to the nature of what you're summing - an exponent of i * the integral of the Lagrangian over each spacetime field configuration. This vary likes crazy so if you skip the some parts you might get a completely different result. The trick to anyhow get anything out of this is to restrict yourself to observables that can be calculated from the ground state, which turn out to be accessible by doing the field integrals over imaginary time instead. This is a trick of calculus, it's not really "non-physical", although it is a pretty crazy method :) This has allowed practitioners to calculate hadron masses for example, it's getting better and better over the decades.