具有虚质量的Dirac哈密顿量和不定度规诱导的螺旋度依赖性
Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric
摘要：
研究自旋1/2粒子的超光速物质波方程的性质具有广泛的理论意义。人们可以通过用实质量项明确地替代虚质量来强制超光速传播，或者可以使用虚单位乘以质量项的矩阵表示。后者导致了快子狄拉克方程，而通过在狄拉克方程中代入m->i*m得到的方程自然被称为无质量狄拉克方程。无论是快子，以及双质量狄拉克哈密顿量与螺旋算子交换。这两种哈密顿量都是伪厄米特的，并且还具有额外的修改后的伪厄米特性质，从而导致对共振本征值的约束。在这里，通过一个明确的计算，我们表明，特定的总和规则的频谱持有相应的波函数定义明确的实能量本征值和复杂的共振和反共振能量。在量子化的双质量狄拉克场中，单粒子态的右手螺旋度获得了一个负范数（“不定度规”），并且可以通过Gupta-Bleeland型条件从物理谱中排除。
英文摘要：
It is of general theoretical interest to investigate the properties of superluminal matter wave equations for 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 the tachyonic 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. Here, by an explicit calculation, we show that specific sum rules over the spectrum hold for the wave functions corresponding to the well-defined real energy eigenvalues and complex resonance and anti-resonance energies. In the quantized imaginary-mass Dirac field, one-particle states of right-handed helicity acquire a negative norm ("indefinite metric") and can be excluded from the physical spectrum by a Gupta--Bleuler type condition.
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