2023
DOI: 10.1142/s0217751x23300028
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Snowmass white paper: The quest to define QFT

Abstract: This paper provides a review of the literature on rigorous definitions and constructions in quantum field theory (QFT), spanning the period of seven decades. Compared with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations. Therefore, it is still an outstanding open problem to formulate a complete definition of QFT. We argue that the question is of relevance for both physicists and mathematicians.

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Cited by 3 publications
(2 citation statements)
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“…The Janus interface interpolates between certain boundary conditions corresponding to the vacua of massless and massive 3d theories. These boundary conditions correspond to equivariant elliptic cohomology classes of the Higgs branch of the 3d theory and the (flavor) torus fixed points of the Higgs branch respectively [72]. The elliptic stable envelope is then seen as a map between these cohomologies (the elliptic version of (0.7)).…”
Section: Spin Chainmentioning
confidence: 99%
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“…The Janus interface interpolates between certain boundary conditions corresponding to the vacua of massless and massive 3d theories. These boundary conditions correspond to equivariant elliptic cohomology classes of the Higgs branch of the 3d theory and the (flavor) torus fixed points of the Higgs branch respectively [72]. The elliptic stable envelope is then seen as a map between these cohomologies (the elliptic version of (0.7)).…”
Section: Spin Chainmentioning
confidence: 99%
“…Next, let us look at all the 3d N = 2 chiral multiplets that survive with Dirichlet boundary conditions. Multiplets receiving Dirichlet at 72) and (4.67)). But everything in M C 1 ;− (p 1 ) receives Neumann at the Janus (4.90) and therefore vanishes in the effective 2d theory.…”
Section: Elliptic Stable Envelopementioning
confidence: 99%