pp-adic Mellin Amplitudes

In this paper, we propose a $p$-adic analog of Mellin amplitudes for scalar operators, and present the computation of the general contact amplitude as well as arbitrary-point tree-level amplitudes for bulk diagrams involving up to three internal lines, and along the way obtain the $p$-adic version of the split representation formula. These amplitudes share noteworthy similarities with the usual (real) Mellin amplitudes for scalars, but are also significantly simpler, admitting closed-form expressions where none are available over the reals. The dramatic simplicity can be attributed to the absence of descendant fields in the $p$-adic formulation.Comment: 60 pages, several figures. v2: Minor typos fixed, references adde

Recursion Relations in pp-adic Mellin Space

In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin-Barnes representation of both real and $p$-adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions.Comment: 45 pages + appendices, several figure

Documentation of animal health in organic pig herds

The health of weaned pigs should be described using several information sources to get an overall assessment of the health state in the herd. In this case study four organic pig herds each fattening between 800 and 3500 pigs per year provided data from clinical examination of a sample of animals, pathological findings at slaughter, post weaning mortality and medicine usage in the herd. Clinical symptoms were present in 8 – 18 % of the pigs, and 2 – 6 % of the pigs showed more serious symptoms of disease. At slaughter 10 – 17 % of the pigs got remarks for pathological lesions, primarily liver spots, abscesses and chronic pericarditis. The post weaning mortality varied between herds, while the usage of medicine was rather low in the herds. The herd health status can be aggregated in many ways. A suggestion is made for the four herds. According to this the good health state is achieved in herds combining a modest medicine usage with a low level of disease, measured by low prevalence of clinical symptoms, low number of remarks at slaughter and low mortality

Cutting the Coon Amplitude

The Coon amplitude is a $q$-deformed generalization of the Veneziano amplitude exhibiting a semi-infinite sequence of poles that converge on an accumulation point, from which a branch cut emerges. A number of recent papers have provided compelling evidence that the residues of this amplitude satisfy the positivity requirements imposed by unitarity. This paper investigates whether positivity is also satisfied along the branch cut. It is found that positivity violations occur in a region of the branch cut exponentially close to the accumulation point according to a scale set by $q$. The closing section of the paper discusses possible interpretations of this fact and strategies for excising negativity from the partial wave coefficients. An appendix presents derivations of instrumental identities relating the $q$-gamma and $q$-polygamma functions to the Weierstrass elliptic and quasiperiodic functions.Comment: v2: fixed typo in equation (55), fixed Figure 1, added two references, made the summary of section 2 in the introduction more precise, edited discussion in second bullet point in section 3

Immune Regulation in Allergic and Irritant Skin Reactions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65499/1/j.1365-4362.1991.tb03844.x.pd

Scattering Equations and Feynman Diagrams

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $\phi^3$-theory. We also discuss the generalization to general scalar field theories with $\phi^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.Comment: 18 pages, 57 figure

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic objects which compute higher-point global (scalar) conformal blocks in arbitrary spacetime dimensions, extending the result for the four-point block, known in the literature as a geodesic Witten diagram, to five- and six-point blocks. The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime. Using the holographic representation of the higher-point conformal blocks and higher-point propagator identities, we develop geodesic diagram techniques to obtain the explicit direct-channel conformal block decomposition of a broad class of higher-point AdS diagrams in a scalar effective bulk theory, with closed-form expressions for the decomposition coefficients. These methods require only certain elementary manipulations and no bulk integration, and furthermore provide quite trivially a simple algebraic origin of the logarithmic singularities of higher-point tree-level AdS diagrams. We also provide a more compact repackaging in terms of the spectral decomposition of the same diagrams, as well as an independent discussion on the closely related but computationally simpler framework over p-adics which admits comparable statements for all previously mentioned results