A Krein quantization approach to Klein paradox

Abstract

In this paper we first introduce the famous Klein paradox. Afterwards by proposing the Krein quantization approach and taking the negative modes into account, we will show that the expected and exact current densities, could be achieved without confronting any paradox.

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

“…Maintaining the negative mode states, we define (8), having κ and κ ′ , one can obtain relations between incident, reflected and transmitted currents for electrons (and positrons) of negative energies. We have Now, we can easily see that maintaining all modes could provides equal values for reflected and transmitted electrons and positrons [42]. According to processes in regions (I) and (II) in Figure 2, and using equation (8) together with (9), one can define M .…”

“…As an application of modified descriptions for entangled (space-time) states, the original version of EPR paradox can be discussed and the correct answer can be verified based on the strong rooted complex quantum Hamilton-Jacobi theory [2-27] and as another example we can use the negative energy states, to remove the Klein's paradox without the need of any further explanations or justifications like backwardly moving electrons. Finally, comparing the two approaches, we can point out to the existence of a connection between quantum Hamiltonian dynamics, standard quantum field theory, and Krein space quantization [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. …”

The Stationary Dirac Equation as a Generalized Pauli Equation for Two Quasiparticles

“…Perhaps, the most paradoxical implications of the Dirac equation are the Klein tunneling [3][4][5][6][7][8][9][10] and the so-called 'Zitterbewegung' phenomenon [3,11,12]. Both are often mentioned in the current literature on this equation and both give rise to controversy among researchers.…”