双复代数的能量宇称
Energy-parity from a bicomplex algebra
摘要：
通过用双复数的交换环来代替复数场，我们试图构造具有正能态和负能态的相互作用标量量子场论。这项工作的地方[R. Dickinson，J. Forshaw和P. Millington，J.Phys.Conf.Ser.631（2015）012059]，并结合了[A. D. Linde，Phys. Lett. B 200（1988）272; D. E. Kaplan和R. Sundrum，JHEP 0607（2006）042]。正能态和负能态的相互作用使得真空能被抵消。正能态和负能态都有正的范数，它们的直接混合被双复数的零因子所阻止，从而消除了负能级联的可能性。我们认为，相同的相互作用的积极和消极的能量状态可能会允许哈格定理被绕过，消除相关的批评福克表示。我们考虑标量理论与立方和四次相互作用，并描述如何这种建设可能会产生符合标准的散射理论的跃迁几率。虽然这些结果是有趣的，我们提请注意潜在的严重限制微扰么正性。
英文摘要：
By replacing the field of complex numbers with the commutative ring of bicomplex numbers, we attempt to construct interacting scalar quantum field theories that feature both positive- and negative-energy states. This work places the tentative ideas proposed in [R. Dickinson, J. Forshaw and P. Millington, J. Phys. Conf. Ser. 631 (2015) 012059] on more solid and general mathematical foundations and incorporates the "energy-parity" symmetry introduced in [A. D. Linde, Phys. Lett. B 200 (1988) 272; D. E. Kaplan and R. Sundrum, JHEP 0607 (2006) 042]. The interplay of the positive- and negative-energy states allows for cancellations of the vacuum energy. Both the positive- and negative-energy states have positive norms, and their direct mixing is prevented by virtue of the zero divisors of the bicomplex numbers, thereby eliminating the possibility of negative-energy cascades. We suggest that the same interplay of positive- and negative-energy states may allow Haag's theorem to be circumvented, removing the associated criticism of the Fock representation. We consider scalar theories with cubic and quartic interactions and describe how this construction may yield transition probabilities consistent with the standard scattering theory. Whilst these results are intriguing, we draw attention to potentially serious limitations in relation to perturbative unitarity.
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