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Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...
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The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
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Updated: Jan 27, 2026

Scattering And Absorption of Light in Planetary Regoliths
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Polarized Scattering Equations for 6D Superamplitudes.

Yvonne Geyer1, Lionel Mason2

  • 1Institute for Advanced Study, 1 Einstein Drive, 08540 Princeton, New Jersey, USA.

Physical Review Letters
|April 2, 2019
PubMed
Summary

We introduce polarized scattering equations incorporating spinor data for new tree-level scattering amplitude formulas in six dimensions. These equations offer a distinct framework for super Yang-Mills theory, gravity, and brane amplitudes.

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Area of Science:

  • High-energy physics
  • Theoretical physics
  • String theory

Background:

  • Scattering equations are fundamental in calculating scattering amplitudes in quantum field theory.
  • Existing methods face challenges in incorporating spinor polarization data and extending to higher dimensions.

Purpose of the Study:

  • To introduce polarized scattering equations, a spinorial generalization of scattering equations.
  • To derive new formulas for tree-level scattering amplitudes in six dimensions.
  • To explore connections with supersymmetry and ambitwistor strings.

Main Methods:

  • Development of spinorial scattering equations incorporating polarization data.
  • Formulation of new tree-level scattering amplitude formulas in six dimensions.
  • Investigation of the ambitwistor string origin of these equations in supertwistor space.

Main Results:

  • Introduction of polarized scattering equations for six-dimensional scattering amplitudes.
  • Formulas directly extendable to maximal supersymmetry.
  • Identification of new integrand ingredients for super Yang-Mills theory, gravity, M5 and D5 branes.
  • Derivation of massive analogues of 4D refined scattering equations upon dimensional reduction.

Conclusions:

  • The polarized scattering equations provide a novel and distinct framework for scattering amplitudes.
  • This framework naturally incorporates spinor polarization and extends to higher dimensions and supersymmetry.
  • The study reveals deep connections between scattering equations, ambitwistor strings, and supertwistor theory.