QFT with twisted Poincaré invariance and the Moyal product
QFT with twisted Poincaré invariance and the Moyal product
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具有扭曲庞加莱不变性的 QFT 和 Moyal 产品
DOI：
10.1088/1126-6708/2007/05/098
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发表时间：
2007
影响因子：
5.4
通讯作者：
J. Mourad
中科院分区：
文献类型：
--
作者：
E. Joung;J. Mourad
我们研究在量子场论中扭转庞加莱不变性的后果。首先，我们构造一个与扭曲兼容的福克空间以及相应的创建和湮灭算子。然后，我们证明了在创建和湮灭算子中线性的协变场不存在。放宽线性条件，可以确定协变场。我们证明它通过酉变换与未扭曲场相关，并且所得的 n 点函数与未扭曲场一致。我们还表明，扭曲对称下的不变性可以通过使用具有通常乘积的协变场或具有 Moyal 乘积的非协变场来实现。所得到的 S 矩阵元素与未扭曲的元素一致，直至动量相关相位。
We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.