text: 400,68,1361577810553356292,270481144,Antoine Tilloy,"I put on arxiv a new paper where I apply the variational method in relativistic quantum field theory in 1+1 dimensions. The novelty is that there is no cutoff, infrared or ultraviolet, as is usually the case, and so the results are truly variational <LINK> The idea is to modify the continuous matrix product states (CMPS) introduced by @fverstraete and Ignacio Cirac in 2010. The CMPS already do the job in the non-relativistic case, but still require a UV cutoff for relativistic QFT. The modification consists in changing of operator basis, to work in one that solves the short distance behavior exactly, and fits the singular UV behavior. This allows to bypass the last of Feynman's objections of 1987 against the variational method in relativistic QFT. The idea is simple, and had been in my head for a while, but I only got the courage to do the (semi-tedious) computations recently. In my opinion, they are not super enlightening except for experts, so I dropped them in a second paper <LINK> @fverstraete Thanks, means a lot! For the entanglement entropy, since I softly break locality, I wouldn't know how to compute the usual one. But it does define a new analogous quantity that should be finite (but not sure if physically meaningful though) @fverstraete Thanks for the reference, I'll have a look @mmanuF In principle, CMPS have a generalization, continuous tensor networks states but it's much more difficult to use and do computations in practice. The renormalization of the Hamiltonian is also trickier in higher dimensions (need more than normal ordering) @mmanuF So to be transparent, right now, I know only how to deal with 1+1 dimensions. There are a number of hurdles to lift before doing higher dimensions. I discuss it a bit at the end of the papers (short and long)",https://arxiv.org/abs/2102.07733,"The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial. ",Variational method in relativistic quantum field theory without cutoff,8,"['I put on arxiv a new paper where I apply the variational method in relativistic quantum field theory in 1+1 dimensions. The novelty is that there is no cutoff, infrared or ultraviolet, as is usually the case, and so the results are truly variational\n\n<LINK>', 'The idea is to modify the continuous matrix product states (CMPS) introduced by @fverstraete and Ignacio Cirac in 2010. The CMPS already do the job in the non-relativistic case, but still require a UV cutoff for relativistic QFT.', ""The modification consists in changing of operator basis, to work in one that solves the short distance behavior exactly, and fits the singular UV behavior. This allows to bypass the last of Feynman's objections of 1987 against the variational method in relativistic QFT."", 'The idea is simple, and had been in my head for a while, but I only got the courage to do the (semi-tedious) computations recently. In my opinion, they are not super enlightening except for experts, so I dropped them in a second paper\n\nhttps://t.co/K0AMyG5tVp', ""@fverstraete Thanks, means a lot! For the entanglement entropy, since I softly break locality, I wouldn't know how to compute the usual one. But it does define a new analogous quantity that should be finite (but not sure if physically meaningful though)"", ""@fverstraete Thanks for the reference, I'll have a look"", ""@mmanuF In principle, CMPS have a generalization, continuous tensor networks states but it's much more difficult to use and do computations in practice. The renormalization of the Hamiltonian is also trickier in higher dimensions (need more than normal ordering)"", '@mmanuF So to be transparent, right now, I know only how to deal with 1+1 dimensions. There are a number of hurdles to lift before doing higher dimensions. I discuss it a bit at the end of the papers (short and long)']",21,02,1789