Coupling fields and underlying space curvature: an augmented Lagrangian approach

Area of Science:

• Theoretical Physics
• Computational Physics
• Mathematical Modeling

Background:

• Coupling between fields and spacetime geometry is crucial in physics.
• Existing models often lack a dynamic feedback mechanism.
• Molecular dynamics simulations offer insights into complex system interactions.

Purpose of the Study:

• To systematically implement and model the feedback between a scalar field and its carrying space's geometry.
• To develop a generalized framework applicable to various physical systems.
• To explore numerical implementations and validate the model.

Main Methods:

• Utilized a generalized Lagrangian incorporating coupling between the metric tensor and scalar field.
• Incorporated terms inspired by Rahman-Parrinello molecular dynamics (RP-MD).
• Developed two implementations: time-dependent metric (ODE) and spatiotemporal metric (PDE).

Main Results:

• Demonstrated a systematic feedback mechanism between scalar fields and geometry.
• Successfully implemented both ODE and PDE models for metric evolution.
• Reported numerical results for a (1+1)-dimensional sine-Gordon model.

Conclusions:

• The proposed model provides a systematic way to study field-geometry feedback.
• The framework is adaptable for different physical scenarios, including those inspired by molecular dynamics.
• Numerical simulations confirm the model's capability in capturing complex dynamics.