Anil K. Trivedi | Searcharxiv

arXiv1993

The Nielsen-Ninomiya ``No-Go'' Theorem is False

The Nielsen-Ninomiya no-go theorem asserts that chiral Weyl~(``neutrino'') fields cannot exist on lattices. However, the actual mathematical arguments advanced in the theorem fail to make that case. The theorem leaves the problem of lattice neutrinos completely open; it identifies no obstacle which would prevent us from discretizing chiral theories. (INFORMAL ABSTRACT: Have you too, like every second person in the field, been citing the Nielsen-Ninomiya theorem but have not read or analyzed it? Then, this paper will wake you up. Reading it is a prerequisite to doing any good work in chiral lattice physics.)

hep-lat↗

arXiv1993

Weyl Neutrinos on a Lattice: An Explicit Construction

Introducing a new and universally applicable discretizing technique, I construct a class of local and unitary lattice theories of Weyl neutrinos; this solves a longstanding and allegedly unsolvable problem in quantum field theory. En route, I also prove a general ``go'' theorem that all Lagrangian-density based continuum quantum field theories can be lattice-regularized. (INFORMAL ABSTRACT: You didn't study the Nielsen-Ninomiya theorem, only trusted the authors to have proven ``the absence of neutrinos on a lattice''. Well, they didn't. Nor can anyone else: every continuum theory can be lattice-regularized. A proof of that, plus an explicit construction of lattice neutrinos: if you read only one paper this year, here it is! From now on, this is how chiral fermions should be latticized. All else is gaslight.)

hep-lat↗