68 research outputs found
Feynman motives
No full textThis book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer.
Two different approaches to the subject are described. The first, a “bottom-up” approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch–Esnault–Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, “top-down” approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann–Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry.
The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area
Homological algebra for Schwartz algebras of reductive p-adic groups
No full textLet G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if G is semi-simple, V and W are tempered irreducible representations of G, and V or W is square-integrable, then Ext G n (V, W) ≅ 0 for all n ≥ 1. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler
Synthesis, Structure, and Second-Order Nonlinear Optical Properties of Copper(II) and Palladium(II) Acentric Complexes with N-Salicylidene-N'-aroylhydrazine Tridentate Ligands.
No full textSynthesis and spectroscopic and NLO properties of "push-pull" structures incorporating the inductive electron-withdrawing pentafluorophenyl group
No full textA series of push-pull mols., each incorporating a pentafluorophenyl ring as an inductive accepting group, has been synthesized. The nonlinear optical properties of these compds. were measured in soln. by EFISH (operating at 1907 nm) and in the solid state by the Kurtz powder technique (at 1907 nm). Values of μβ, the product of the mol. dipole moment and its first-order hyperpolarizability, of up to 200 × 10-48 esu were obtained
Oxalic acid as a heterogeneous ice nucleus in the upper troposphere and its indirect aerosol effect
No full textZobrist B, Marcolli C, Koop T, et al. Oxalic acid as a heterogeneous ice nucleus in the upper troposphere and its indirect aerosol effect. ATMOSPHERIC CHEMISTRY AND PHYSICS. 2006;6(10):3115-3129.Heterogeneous ice freezing points of aqueous solutions containing various immersed solid dicarboxylic acids (oxalic, adipic, succinic, phthalic and fumaric) have been measured with a differential scanning calorimeter. The results show that only the dihydrate of oxalic acid (OAD) acts as a heterogeneous ice nucleus, with an increase in freezing temperature between 2 and 5 K depending on solution composition. In several field campaigns, oxalic acid enriched particles have been detected in the upper troposphere with single particle aerosol mass spectrometry. Simulations with a microphysical box model indicate that the presence of OAD may reduce the ice particle number density in cirrus clouds by up to ~50% when compared to exclusively homogeneous cirrus formation without OAD. Using the ECHAM4 climate model we estimate the global net radiative effect caused by this heterogeneous freezing to result in a cooling as high as −0.3 Wm−2
Do atmospheric aerosols form glasses?
No full textZobrist B, Marcolli C, Pedernera DA, Koop T. Do atmospheric aerosols form glasses? ATMOSPHERIC CHEMISTRY AND PHYSICS. 2008;8(17):5221-5244.A new process is presented by which water soluble organics might influence ice nucleation, ice growth, chemical reactions and water uptake of aerosols in the upper troposphere: the formation of glassy aerosol particles. Glasses are disordered amorphous (non-crystalline) solids that form when a liquid is cooled without crystallization until the viscosity increases exponentially and molecular diffusion practically ceases. The glass transition temperatures, Tg, homogeneous ice nucleation temperatures, Thom, and ice melting temperatures, Tm, of various aqueous inorganic, organic and multi-component solutions are investigated with a differential scanning calorimeter. The investigated solutes are: various polyols, glucose, raffinose, levoglucosan, an aromatic compound, sulfuric acid, ammonium bisulfate and mixtures of dicarboxylic acids (M5), of dicarboxylic acids and ammonium sulfate (M5AS), of two polyols, of glucose and ammonium nitrate, and of raffinose and M5AS. The results indicate that aqueous solutions of the investigated inorganic solutes show Tg values that are too low to be of atmospheric importance. In contrast, aqueous organic and multi-component solutions readily form glasses at low but atmospherically relevant temperatures (≤230 K). To apply the laboratory data to the atmospheric situation, the measured phase transition temperatures were transformed from a concentration to a water activity scale by extrapolating water activities determined between 252 K and 313 K to lower temperatures. The obtained state diagrams reveal that the higher the molar mass of the aqueous organic or multi-component solutes, the higher Tg of their respective solutions at a given water activity. To a lesser extent, Tg also depends on the hydrophilicity of the organic solutes. Therefore, aerosol particles containing larger (≳150 g mol−1) and more hydrophobic organic molecules are more likely to form glasses at intermediate to high relative humidities in the upper troposphere. Our results suggest that the water uptake of aerosols, heterogeneous chemical reactions in aerosol particles, as well as ice nucleation and ice crystal growth can be significantly impeded or even completely inhibited in organic-enriched aerosols at upper tropospheric temperatures with implications for cirrus cloud formation and upper tropospheric relative humidity
Synthesis, Structure, and Second-Order Nonlinear Optical Properties of Copper(II) and Palladium(II) Acentric Complexes with N-Salicylidene-N'-aroylhydrazine Tridentate Ligands.
No full textSynthesis, Structure, and Second-Order Nonlinear Optical Properties of Copper(II) and Palladium(II) Acentric Complexes with N-Salicylidene-N'-aroylhydrazine Tridentate Ligands.
No full textSpectral action gravity and cosmological models
No full textThis paper surveys recent work of the author and collaborators on cosmological models based on the spectral action functional of gravity. A more detailed presentation of the topics surveyed here will be available in a forthcoming book [1]
Information Algebras and Their Applications
No full textIn this lecture we will present joint work with Ryan Thorngren on thermodynamic semirings and entropy operads, with Nicolas Tedeschi on Birkhoff factorization in thermodynamic semirings, ongoing work with Marcus Bintz on tropicalization of Feynman graph hypersurfaces and Potts model hypersurfaces, and their thermodynamic deformations, and ongoing work by the author on applications of thermodynamic semirings to models of morphology and syntax in Computational Linguistics
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