The discussion revolves around the electron gyromagnetic ratio and its computation using perturbative and non-perturbative methods in quantum field theory (QFT). Participants explore the feasibility of lattice QFT for precise calculations, alternative non-perturbative approaches, and the implications of quantum corrections and fine-tuning in the context of the Higgs hierarchy problem.
Participants express multiple competing views on the applicability of lattice QFT for precise calculations and the implications of non-perturbative methods. The discussion on fine-tuning and naturalness also reveals differing perspectives, with no consensus reached.
Limitations include the dependence on computational power for lattice QFT, the unresolved nature of quantum corrections in non-perturbative contexts, and the ambiguity surrounding the definitions of fine-tuning and naturalness.
Demystifier said:With presently existing computer power, lattice calculations are not suitable for very precise computations in 3+1 dimensions. For that reason, g-2 is not a quantity suitable for a lattice treatment. It can be computed in principle, but in practice it cannot be computed with such a big precision.
Some of the approaches are partial resummation of perturbative expansion, effective theory modeling, lower dimensional analogues, axiomatic approaches, ...star apple said:What is other non-perturbative approach other than lattice QFT?
Demystifier said:Some of the approaches are partial resummation of perturbative expansion, effective theory modeling, lower dimensional analogues, axiomatic approaches, ...
Yes we would.star apple said:Say.. about the Higgs Hierarchy Problems (https://en.wikipedia.org/wiki/Hierarchy_problem).. would we still have the same problem if we use non-perturbative QFT?
Demystifier said:Yes we would.
You mix up some independent concepts such as quantum correction, perturbation and renormalization. Any of these concepts can make sense without the others.star apple said:Oh.. why is there still "quantum corrections" in non-perturbative QFT? Is it not the Hierarchy Problem is due to the quantum corrections.. so what is the counterpart of "quantum corrections" in non-perturbative QFT?
Perturbative means it is Taylor expansion and since we can't solve the higher order of the coupling constants. So we renormalize to lower power and eliminate the higher power. Does Non-perturbative means we can solve the higher power? But if it is infinite.. how can non-perturbation solve it?
Demystifier said:You mix up some independent concepts such as quantum correction, perturbation and renormalization. Any of these concepts can make sense without the others.
Demystifier said:You mix up some independent concepts such as quantum correction, perturbation and renormalization. Any of these concepts can make sense without the others.
Finetuning and naturalness are not artifacts of doing perturbation theory.star apple said:To which extent is finetuning (and hence naturalness) an artefact of doing perturbation theory?
I'm sure there are, but I am not an expert in exactly solvable QFT's so I cannot give a concrete example.star apple said:Are there exactly soluble QFT's which suffer from naturalness/finetuning problems? Others are asking this same questions too.
Demystifier said:Finetuning and naturalness are not artifacts of doing perturbation theory.
I'm sure there are, but I am not an expert in exactly solvable QFT's so I cannot give a concrete example.
For instance, if you study SM on the lattice, you have to choose some UV cutoff on the lattice. The physical quantities may strongly depend on that choice, which can lead to a fine tuning problem.star apple said:Ah, ok. how would finetuning of the Higgs mass show up in a non-perturbative formulation of the SM? Thanks a lot.