Phase Space Formalism Simplifies Scattering Amplitudes, Automating Reductions up to Six Points

Scattering amplitudes, the mathematical heart of particle physics calculations, present formidable challenges for even the most powerful computers. Joon-Hwi Kim from the California Institute of Technology and colleagues now present a novel approach to calculating these amplitudes, employing a technique called worldline formalism within the framework of phase space. This method reveals underlying symmetries and simplifies complex calculations, automating key steps traditionally performed by hand and offering a potentially significant speedup for future research. The team demonstrates the power of this new framework by successfully calculating multi-Compton amplitudes, and extending the approach to Yang-Mills theory and gravity, suggesting a versatile tool for tackling increasingly complex problems in theoretical physics. This work establishes a foundation for more efficient calculations and a deeper understanding of fundamental interactions.

Employing non-canonical coordinates simplifies the rules governing scattering amplitude calculations and clearly demonstrates gauge invariance, allowing the research to navigate the boundary conditions within phase space and correctly identify associated mathematical spaces. This approach establishes a phase space implementation optimised for computing scattering amplitudes while preserving the strengths of the original formalism. To demonstrate this capability, the researchers compute multi-photon Compton amplitudes up to six points in the classical limit, and extend this to Yang-Mills theory and gravity by assuming backgrounds of nonlinearly superposed plane waves.

Scattering Amplitudes, Gravity, and Worldline Methods

This extensive list of references details a deep exploration of theoretical physics, specifically focusing on scattering amplitudes, gravity, string theory, and the worldline formalism, underpinned by mathematical structures like symplectic and differential geometry. Key themes include the double copy, a relationship between gauge theory and gravity, and color-kinematics duality, a crucial ingredient in this connection.

Phase Space Simplifies Scattering Amplitude Calculations

Scientists have developed a novel approach to calculating scattering amplitudes in particle physics, leveraging the mathematical framework of phase space and worldline formalism. This method establishes a connection between symplectic geometry and particle behavior, revealing universal features within the underlying mathematical structures. The team discovered that by employing non-compact topologies within the phase space, they could automate complex calculations, essential for determining particle interactions, while adhering to the boundary conditions inherent in phase space calculations. The research demonstrates that utilizing non-canonical coordinates simplifies the mathematical rules governing these calculations, explicitly manifesting gauge invariance, a fundamental principle ensuring the consistency of physical theories.

This phase space implementation offers a potentially optimized framework for calculating scattering amplitudes while retaining the benefits of the original worldline formalism. To demonstrate its effectiveness, scientists successfully calculated multi-Compton amplitudes, describing the scattering of photons, up to six points in the classical limit, and extended this approach to Yang-Mills theory and gravity by considering backgrounds of superposed plane waves. Furthermore, the team showed that this method naturally accommodates spinning black holes, often requiring the use of non-canonical coordinates, and provides a systematic way to treat both gauge theory and gravity. The findings confirm the versatility of this approach, as it can be applied to various perturbative worldline frameworks, including those used to calculate impulse and recoil operators, and explore double copy structures, relationships between different physical theories. This breakthrough delivers a powerful new tool for theoretical physicists, offering a streamlined and geometrically insightful method for tackling complex calculations in particle physics and gravity.

Phase Space Simplifies Scattering Amplitude Calculations

This research presents a new implementation of the worldline formalism, a technique used in scattering amplitude calculations, but adapted to operate within phase space, the space of all possible positions and momenta. The approach leverages the geometric properties of phase space, specifically symplectic geometry, to simplify calculations and reveal underlying structures. Notably, the method automatically incorporates certain reductions necessary for obtaining physical results, streamlining the process of relating theoretical calculations to observable quantities. The researchers demonstrate the effectiveness of this phase space implementation by applying it to multi-Compton amplitudes, calculations describing the scattering of particles, extending up to six points in the classical limit, and also to scenarios involving Yang-Mills theory and gravity.

The results indicate that this framework offers a potentially optimized method for calculating scattering amplitudes while retaining the benefits of the original worldline formalism. The authors acknowledge a recent, independent discovery of a related connection between worldline topologies and LSZ reduction, though their approach differs in its derivation, stemming from a pursuit of gauge invariance within phase space. Future work could explore the full potential of this framework for more complex calculations and its connections to other areas of theoretical physics.