An Overview of Long-Range Casimir Interactions

Casimir's entropy

“…The analysis can be viewed alternatively as follows. Given that the thermal occupancy is given by the Bose expression (7), we may calculate the Casimir thermal energy without the zero-point fluctuations contribution. Now at high T we have (cf equation (19)) as the energy tied to a mode,…”

“…Cosmological implications are considered to be due to the finiteness of the universe [4]. The literature on the subject is vast, as is attested to in [4][5][6][7][8]. The vacuum for the electromagnetic field may be considered as its equilibrium state in the limit of vanishing temperature (T ).…”

Analytical on-shell calculation of low energy higher order scattering

“…The calculation of scattering amplitudes is a staple of theoretical physics, and recently a number of investigations have been reported which study higher order effects in electromagnetic scattering [1][2][3][4], gravitational scattering [5][6][7][8][9][10][11] and both [12][13][14].…”

“…and nonrelativistic amplitudes are defined by taking the low energy limit and dividing the covariant forms by the normalizing factor 2 It is interesting to note that this method is essentially the one used by Feynman in his seminal paper, wherein he quantized gravity and realized the need for the introduction of ghosts [15].…”

On Expansion of a Spherical Enclosure Bathed in Zero-Point Radiation

“…To obtain physically meaningful figures from it a rather laborious work with infinities is necessary, the aim of which is usually to evaluate finite differences between infinite ZP energy deposited in free space and infinite electromagnetic energy resulting from the redistribution of the ZP spectrum into normal modes corresponding to given boundaries. For example, an astonishingly good prediction of forces existing between two infinite perfectly conducting planes [6,7] (so called Casimir's effect) was obtained just by computing a finite difference of two infinite radiation forces acting on different sides of the said planes. It is a remarkable consequence of the vector character of electromagnetic field [5] that the corresponding mathematical procedure enables exact cancellation of high frequency modes without introduction of a frequency cut-off.…”