Homology and Feynman integrals

Feynman diagram
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elearning.gau.ge/change-lessons-from-the-ceo-real-people-real.php Finally, we show that our diagrammatic coaction follows, in the special case of one-loop integrals, from a more general coaction proposed recently, which is constructed by pairing master integrands with corresponding master contours. Skip to main content. User menu Cart Login.

Analytic Properties of Feynman Diagrams in Quantum Field Theory

Search form Search. Goncharov A. Panzer, Feynman integrals and hyperlogarithms, Ph. Thesis, Humboldt University, Berlin, Inst. Bogner Christian, MPL—A program for computations with iterated integrals on moduli spaces of curves of genus zero , Caffo, H. Czyz, S. Laporta and E. Remiddi, The master differential equations for the two loop sunrise selfmass amplitudes, Nuovo Cim.

Adams, C. Bogner and S. Weinzierl, The iterated structure of the all-order result for the two-loop sunrise integral, J. Bloch, M. Kerr and P. Vanhove, Local mirror symmetry and the sunset Feynman integral, arXiv The two-loop massive sunrise and the kite integral , An application to the three-loop massive banana graph , Brown, On the decomposition of motivic multiple zeta values, arXiv Duhr Claude, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes , Kreimer, The core Hopf algebra, Clay Math. Brown, Notes on motivic periods, arXiv Abreu, R.

The quaternions and Bott periodicity are quantum Hamiltonian reductions.

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Symmetry, Integrability and Geometry: Methods and Applications , 12 , , 6 pages. Journal of homotopy and related structures , June , Volume 11, Issue 2, pp — Focusing on the case of S 1 , this paper studies the question of whether this commutative Frobenius algebra structure lifts to a "homotopy" commutative Frobenius algebra structure at the cochain level, under a mild locality-type condition called "quasilocality".

The answer turns out to depend on the choice of context in which to do homotopy algebra — there are two reasonable worlds in which to study structures like Frobenius algebras that involve many-to-many operations. If one works at "tree level", we prove that there is a homotopically-unique quasilocal cochain-level homotopy Frobenius algebra structure lifting the Frobenius algebra structure on cohomology.

However, if one works instead at "graph level", we prove that a quasilocal lift does not exist. Homological perturbation theory for nonperturbative integrals. Suppose s is generic of degree d. Thus concentration onto the critical locus is not only a perturbative phenomenon. Reflexivity and dualizability in categorified linear algebra. With Martin Brandenburg and Alexandru Chirvasitu. Theory and Applications of Categories , Vol.

We study the questions of when a cocomplete linear category is reflexive equivalent to its double dual or dualizable the pairing with its dual comes with a corresponding copairing. Our main results are that the category of comodules for a countable-dimensional coassociative coalgebra is always reflexive, but without any dimension hypothesis dualizable if and only if it has enough projectives, which rarely happens.

Finally we prove tensoriality a type of Tannakian duality for affine ind-schemes with countable indexing poset.

Poisson AKSZ theories and their quantizations. Abstract: We generalize the AKSZ construction of topological field theories to allow the target manifolds to have possibly-degenerate homotopy Poisson structures. Classical AKSZ theories, which exist for all oriented spacetimes, are described in terms of dioperads. The quantization problem is posed in terms of extending from dioperads to properads. We conclude by relating the quantization problem for AKSZ theories on R d to the formality of the E d operad, and conjecture a properadic description of the space of E d formality quasiisomorphisms.

The fundamental pro-groupoid of an affine 2-scheme. With Alex Chirvasitu. Applied Categorical Structures , Vol 21, Issue 5 , pp. Abstract: A natural question in the theory of Tannakian categories is: What if you don't remember Forget? The formal path integral and quantum mechanics. Journal of Mathematical Physics , 51, We compute this expansion and show that it is formally, if there are ultraviolet divergences invariant under volume-preserving changes of coordinates.

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We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a "Fubini theorem" expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous-quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order.

Thus, by "cutting and pasting" and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic "formal path integral" for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field. Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics.

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We draw one bold point in the middle of a propagation line: it will become the tadpole tail of a new second-order diagram; of course we can draw a bold point in three different positions 15 , so that we should built three new different second-order quantum many-body theory diagrams, starting from the first-order shell one. In: Mathematical Approaches to International Relations, Heisenberg-picture quantum field theory. Keywords: Feynman Diagrams ; Rooted maps ; Many-body systems. Hence one might conjecture that Feynman diagrams and rooted maps are the same topological object.

These results justify the heuristic expansion of Feynman's path integral in diagrams. Supersymmetry and the Suzuki chain. We discover two infinite families and nine exceptional examples.

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The exceptions are all related to the Leech lattice: their automorphism groups are the larger groups in the Suzuki chain Co 1 , Suz:2, G 2 4 :2, J 2 :2, U 3 3 :2 and certain large centralizers therein 2 10 :M 12 :2, M 12 :2, U 4 3 :D 8 , M 21 :2 2. Condensations in higher categories.

Abstract: We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces the idempotents in the ordinary version with a notion that we call "condensations.

We also identify our higher Karoubi envelopes with categories of fully-dualizable objects. Together with the Cobordism Hypothesis, we argue that this realizes an equivalence between a very broad class of gapped topological phases of matter and fully extended topological field theories, in any number of dimensions.

Mock modularity and a secondary elliptic genus. Share Give access Share full text access. Share full text access.

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