Pairwise summation approximation of Casimir energy from first principles

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Electromagnetism

Background:

• The Casimir effect describes a physical force acting between two uncharged conductive bodies, arising from quantum fluctuations of the electromagnetic field.
• The pairwise summation approximation (PSA) is a method used to calculate the Casimir energy, particularly for systems with multiple interacting bodies.

Purpose of the Study:

• To derive the pairwise summation approximation (PSA) for Casimir energy from first principles.
• To determine the validity and limits of the PSA for soft dielectric and soft diamagnetic materials.
• To obtain the PSA for the electromagnetic coupling component of the Casimir energy, thereby completing the PSA for the entire electromagnetic field.

Main Methods:

• Derivation of the PSA for Casimir energy using first-principles calculations.
• Analysis of the soft dielectric and soft diamagnetic limits.
• Calculation of the PSA for the electromagnetic coupling part of the Casimir energy.

Main Results:

• The pairwise summation approximation (PSA) for Casimir energy was obtained from first principles.
• The PSA was found to be an asymptotic approximation valid for large separations between objects.
• The PSA was successfully obtained for the electromagnetic coupling part, completing the PSA limit for the complete electromagnetic field.

Conclusions:

• The pairwise summation approximation (PSA) is a valid method for calculating Casimir energy at large distances.
• This work provides a complete derivation of the PSA for the Casimir energy in the context of soft dielectric and diamagnetic materials.
• The findings advance the understanding of Casimir forces in various material contexts.