Nonlinearly Self-Interacting Extended Bodies Move as Test Bodies in Effective External Fields

Area of Science:

• Theoretical Physics
• General Relativity
• Electromagnetism
• Field Theory

Background:

• Previous work established Detweiler-Whiting prescriptions for test bodies to derive laws of motion for self-interacting bodies.
• These prescriptions involve replacing fields with effective fields, acting as a regularization in the point-particle limit.
• Existing methods are limited to specific contexts like linearized general relativity and electromagnetism.

Purpose of the Study:

• To generalize Detweiler-Whiting prescriptions for extended bodies in nonlinear field theories.
• To develop a formalism for directly deriving these prescriptions for complex systems.
• To incorporate self-force, self-torque, and extended-body effects into equations of motion.

Main Methods:

• Developed a generalized formalism for applying Detweiler-Whiting prescriptions to extended bodies.
• Constructed a generating functional with specific properties.
• Derived effective linear and angular momenta evolving via Mathisson-Papapetrou-Dixon equations.

Main Results:

• Successfully generalized Detweiler-Whiting prescriptions for extended bodies in nonlinear field theories.
• Derived effective equations of motion that implicitly include self-force, self-torque, and extended-body effects.
• Demonstrated the applicability of the formalism to bodies coupled to nonlinear scalar fields and noted gravitational implications.

Conclusions:

• The developed formalism provides a direct method for deriving effective laws of motion for extended bodies.
• This approach unifies the treatment of self-interaction and extended-body dynamics across various field theories.
• The findings offer a significant advancement in understanding the dynamics of self-interacting extended bodies in fundamental physics.