Power spectrum and minimum velocity threshold to generate Cherenkov radiation from the quantum field theory perspective
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Abstract
The theoretical study of Cherenkov radiation (CR) has been developing consistently from classical electrodynamics to quantum field theory. Electrodynamics theory has been popularly applied in the study of CR phenomena since the mid-20th century. The quantum field theory has been slightly utilized in CR, especially in the areas of power spectrum and velocity threshold. This paper aims to calculate the power spectrum of CR by applying quantum field theory and identifying the minimum velocity threshold necessary to generate CR in a water medium. The first step is to calculate the power spectrum of charged particles in the dielectric medium with quantum field theory perspectives by using the Poisson distribution and vacuum persistence probability. After deriving the power spectrum, the minimum velocity of CR can be directly calculated. The second step, the numerical calculation method has been performed to illustrate the minimum velocity threshold of the electron to produce CR in a water medium. The minimum velocity threshold required to generate CR is ( is the speed of light), which equals values of the result from the electrodynamic theory. The last step, a comparison of the Cherenkov power spectrum as derived from electrodynamic theory and quantum field theory, found that both theories are similar results at low angular frequencies but inconsistent results at angular frequencies higher than . This study demonstrates the potential of the quantum field theory for calculating the power spectrum of CR. The result may contribute to the knowledge of theoretical physics including future applications.
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