Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field. (English) Zbl 1026.81041
Summary: The Klein-Gordon and Dirac equations in a semi-infinite lab \((x> 0)\), in the background metric \(ds^2= u^2(x)(- dt^2+ dx^2)+ dy^2+ dz^2\), are investigated. The resulting equations are studied for the special case \(u(x)= 1+ gx\). It is shown that in the case of zero transverse-momentum, the square of the energy eigenvalues of the spin-1/2 particles are less than the squares of the corresponding eigenvalues of spin-0 particles with same masses, by an amount of \(mg\hbar c\). Finally, for non-zero transverse-momentum, the energy eigenvalues corresponding to large quantum numbers are obtained and the results for spin-0 and spin-1/2 particles are compared to each other.
MSC:
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81V17 | Gravitational interaction in quantum theory |
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