2019/08/13 by Cyril Belardinelli, Belardinelli, Cyril · 1 citation
Physics and Astronomy · #Experimental and Theoretical Physics Studies #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.1908.05226
In the present paper the author evaluates the path integral of a charged anisotropic Harmonic Oscillator (HO) in crossed electric and magnetic fields by two alternative methods. Both methods enable a rather formal calculation and circumvent some mathematical delicate issues such as the occurrence of an infinite Normalization constant and ambiguities with path integral calculations when magnetic fields are present. The \emph1st method uses complex Fourier series and a regularization scheme via the Riemann-ζ-function. The \emph2nd method evaluates the path integral by transforming the Lagrangian to a uniformly rotating system. The latter method uses the fact that the Lorentz- and Coriolis force have the same functional form. Both forces cancel each other within the rotating system given that it rotates with Larmor frequency ωL. This fact simplifies considerably the calculation of the path integral.