Negative Energies in the Dirac Equation
Negative Energies in the Dirac Equation
复制标题
狄拉克方程中的负能量
DOI：
10.1515/zna-2015-0494
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
V. Dvoeglazov
中科院分区：
文献类型：
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作者：
V. Dvoeglazov
对于u-和v- 4-旋量，很容易检验代数方程Det（p^ − m）= 0 $Det（\hat p\，- \，m）\，=\，0 $和Det（p^ + m）= 0 $Det（\hat p\，+ \，m）\，=\，0 $都有p0 = ±Ep = ± p2 + m2的解。${p_0}\，= \，\pm {E_p}\，= \，\pm \，\sqrt {\bf{p}}^2}\，+ \，{m^2}} .$对于更高自旋的方程也是如此。同时，每一本书都只考虑（1/2，0）<$（0，1/2）表示的u-旋量和v-旋量的等式p0=Ep，从而应用狄拉克-费曼-施图克尔伯格程序消除负能量解。最近Ziino的作品（以及其他几篇独立的文章）表明，Fock空间可以加倍。我们重新考虑这种可能性的量子场水平上的s=1/2和更高的自旋粒子。
Abstract It is easy to check that both algebraic equation Det(p^ − m) = 0 $Det(\hat p\, - \,m)\, = \,0$ and Det(p^ + m) = 0 $Det(\hat p\, + \,m)\, = \,0$ for u– and v– 4-spinors have solutions with p0 = ±Ep = ± p2 + m2. ${p_0}\, = \, \pm {E_p}\, = \, \pm \,\sqrt {{{\bf{p}}^2}\, + \,{m^2}} .$ The same is true for higher-spin equations. Meanwhile, every book considers the equality p0=Ep for both u– and v– spinors of the (1/2, 0)⊕(0, 1/2) representation only, thus applying the Dirac–Feynman–Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We reconsider this possibility on the quantum field level for both s=1/2 and higher-spin particles.