Casimir energy of a dilute dielectric ball in the mode summation method

Abstract

In the $({\epsilon }_1-{\epsilon }_2{)}^2$--approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a closed form the sum over the angular momentum before the integration over the imaginary frequencies. The linear in $({\epsilon }_1-{\epsilon }_2)$ contribution into the vacuum energy is removed by an appropriate subtraction. The role of the contact terms used in other approaches to this problem is elucidated.

14 pages, REVTeX, no figures, no tables; presentation is made better, new references are added

References in corpus (3)

• Casimir's energy of a conducting sphere and of a dilute dielectric ball
• Casimir energy of a compact cylinder under the condition $\epsilon \mu =c^{-2}$
• Casimir energy of a dilute dielectric ball with uniform velocity of light at finite temperature

Cited by in corpus (10)

• Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method
• Calculating Casimir Energies in Renormalizable Quantum Field Theory
• Casimir effect in quadratic theories of gravity
• Casimir effect in Post-Newtonian Gravity with Lorentz-violation
• Casimir effect in Extended Theories of Gravity
• Casimir effect for a dilute dielectric ball at finite temperature
• Self-Stress on a Dielectric Ball and Casimir-Polder Forces
• Flavor vacuum entanglement in boson mixing
• Casimir energy of a dilute dielectric ball at zero and finite temperature
• On the possibility of the implicit renormalization procedure for the Casimir energy