Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
نویسندگان
چکیده
We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family graph building operators $H_\alpha$ ladder diagrams is constructed and investigated. The complete set eigenfunctions corresponding eigenvalues are found. This enables us explicitly express a wide class four-point general two-loop propagator-type master diagram (with arbitrary indices on lines) as Mellin-Barnes-type integrals. Special cases these evaluated. certain zig-zag two-point planar (relevant bi-scalar $D$-dimensional "fishnet" field theory calculation $\beta$-function in $\phi^4$-theory) considered. convenient integral representations obtained. explicit form fixed by conformal symmetry coincide with 3-point correlation functions theories. By means this approach, we exactly evaluate series special cases. In particular, find fairly simple derivation values multi-loop $D=4$. role especially connection considered invariant solutions Yang-Baxter equation investigated detail.
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2023
ISSN: ['1127-2236', '1126-6708', '1029-8479']
DOI: https://doi.org/10.1007/jhep06(2023)059