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Area of Science:

  • Theoretical Physics
  • High-Energy Physics
  • Mathematical Physics

Background:

  • Existing field space geometries struggle with higher-derivative terms in scalar field theories.
  • Calculating scattering amplitudes in these theories presents significant mathematical challenges.

Purpose of the Study:

  • To develop a generalized field space geometry applicable to higher-derivative scalar field theories.
  • To express scattering amplitudes using a covariant geometry on the all-order jet bundle.

Main Methods:

  • Incorporating spacetime and field derivative coordinates into the geometric framework.
  • Identifying a jet bundle analog to the field space metric.
  • Demonstrating invariance under total derivatives for the metric and its amplitude contributions.

Main Results:

  • A generalized field space geometry that accommodates higher-derivative scalar field theories.
  • A method to express scattering amplitudes via covariant jet bundle geometry.
  • A novel field space metric invariant under field redefinitions and total derivatives.

Conclusions:

  • The developed geometry offers a robust framework for analyzing higher-derivative scalar field theories.
  • This approach simplifies the computation of scattering amplitudes by leveraging jet bundle geometry.
  • The identified metric and its invariance properties provide a powerful tool for theoretical physics research.