Classical and quantum theory of the massive spin-two field

详细信息    查看全文

• 作者：Adrian Koenigstein^a ; ^b ; ^{koenigstein@th.physik.uni-frankfurt.de" class="auth_mail" title="E-mail the corresponding author} ; Francesco Giacosa^a ; ^c ; Dirk H. Rischke^a
• 关键词：Massive spin-two field ; Classical field theory ; Quantum field theory ; Casimir operator ; Commutation relations
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：368
• 期：Complete
• 页码：16-55
• 全文大小：541 K

文摘

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers 16000385&_mathId=si1.gif&_user=111111111&_pii=S0003491616000385&_rdoc=1&_issn=00034916&md5=abd4cd959bb64cf73ee0ae28c9baebf9" title="Click to view the MathML source">J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.