1201.6300 (U. D. Jentschura)

Dirac Equation with Imaginary Mass and Helicity-Dependence    [PDF]

U. D. Jentschura

In the matter wave equations describing spin one-half particles, one can
either enforce superluminal propagation by an explicit substitution of the real
mass term for an imaginary mass, or one can use a matrix representation of the
imaginary unit that multiplies the mass term. The latter leads to thetachyonic
Dirac equation, while the equation obtained by the substitution m -> i*m in the
Dirac equation is naturally referred to as the imaginary-mass Dirac equation.
Both the tachyonic as well as the imaginary-mass Dirac Hamiltonians commute
with the helicity operator. Both Hamiltonians are pseudo-Hermitian and also
possess additional modified pseudo-Hermitian properties, leading to constraints
on the resonance eigenvalues. The spectrum is found to consist of well-defined
real energy eigenvalues and complex resonance and anti-resonance energies. The
quantization of the tachyonic Dirac field has recently been discussed, and we
here supplement a discussion of the quantized imaginary-mass Dirac field. Just
as for the tachyonic Dirac Hamiltonian, we find that one-particle states of
right-handed helicity acquire a negative norm and can be excluded from the
physical spectrum by a Gupta--Bleuler type condition. This observation may
indicate a deeper, general connection of superluminal propagation and
helicity-dependent interactions.

View original: http://arxiv.org/abs/1201.6300