相关论文: Position Space Feynman quadrics and their motives

Motivated by some computations of Feynman integrals and certain conjectures on mixed Tate motives, Bejleri and Marcolli posed questions about the $\mathbb{F}_1$-structure (in the sense of torification) on the complement of a hyperplane…

We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into mixed Tate…

The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincar\'e algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In…

Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of…

We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and propose their conjectural description. We suggest how they should be related to mixed Tate motives over dual numbers for F.

In the Symmetries of Feynman Integrals (SFI) approach, a diagram's parameter space is foliated by orbits of a Lie group associated with the diagram. SFI is related to the important methods of Integrations By Parts and of Differential…

As a higher genus version of universal mixed elliptic motives by Hain and Matsumoto, we consider mixed Teichm\"uller motives as certain motivic local systems on the moduli space of pointed curves. We show that the category of mixed…

Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…

We show that the space of symmetric matrices of a fixed rank $k$ over a field $K$ of characteristic not equal to $2$ is split Tate. We do this by promoting the point-counting strategy of MacWilliams over finite fields to a filtration of the…

It is well known that real points of the Study quadric (sliced along a 3-dimensional generator space) correspond to displacements of the Euclidean 3-space. But we still lack of a kinematic meaning for the points of the ambient 7-dimensional…

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…

We describe an efficient position space technique to calculate lattice Feynman integrals in infinite volume. The method applies to diagrams with massless propagators. For illustration a set of two-loop integrals is worked out explicitly. An…

We give the first examples of finite groups G such that the Chow ring of the classifying space BG depends on the base field, even for fields containing the algebraic closure of Q. As a tool, we give several characterizations of the…

Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…

We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…

We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the…

In this article we study the subgroup of the Picard group of Voevodsky's category of geometric motives generated by the reduced motives of affine quadrics. Our main tools here are the functors of Bachmann, but we also provide an alternative…

Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one momentum…

We study smooth quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$ parameterising $6 \times 6$ skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian $\mathbb{G}(1,5)$. Such surfaces correspond to…