Title: On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces Show Chinese title

Title: 关于闵可夫斯基空间中（不可约）混合反对称高整数自旋场的拉格朗日形式化

Abstract: We extend the results of Lagrangian formulations study to construct gauge-invariant Lagrangians for (ir)reducible integer higher-spin massless and massive representations of the Poincare group with a Young tableau $Y[\hat{s}_1,\hat{s}_2,\hat{s}_3]$ in $d$-dimensional flat space-time (as the probable candidates to describe the Dark Matter problem beyond the SM). These particles are described within a metric-like formulation by tensor fields with 3 groups of antisymmetric Lorentz indices $\Phi_{\mu^1[{\hat{s}_1}],\mu^2[{\hat{s}_2}], \mu^3[{\hat{s}_3}]}$ on a basis of the BRST method with complete, $Q$, and incomplete, $Q_c$, BRST operators. We found unconstrained (with $Q$) and constrained (with $Q_c$ and off-shell BRST invariant holonomic constraints) gauge Lagrangian formulations with different configuration spaces and reducibility stages. The deformation procedure to construct interacting gauge model with mixed-antisymmetric fields is proposed. Show Chinese abstract

Abstract: 我们将拉格朗日公式的研究结果扩展，以构建庞加莱群的(不可约)整数高自旋无质量及有质量表示的规范不变拉格朗日量，其对应的杨图是$Y[\hat{s}_1,\hat{s}_2,\hat{s}_3]$在$d$维平直时空中的（作为可能描述超出标准模型的暗物质问题的候选者）。这些粒子通过具有三组反对称洛伦兹指标的张量场在度规类似形式中进行描述，$\Phi_{\mu^1[{\hat{s}_1}],\mu^2[{\hat{s}_2}], \mu^3[{\hat{s}_3}]}$基于完整的$Q$和不完整的$Q_c$BRST 算子的 BRST 方法。我们发现了无约束的（具有$Q$）和有约束的（具有$Q_c$和非壳上 BRST 不变的正则约束）规范拉格朗日公式，具有不同的配置空间和可约性阶段。提出了构造具有混合反对称场的相互作用规范模型的变形过程。