We study the problem of stability in Podolsky's generalized electrodynamics by constructing a series of 2-parametric bounded conserved quantities. In this way, we show that the 00-component of the energy-momentum tensors could be positive definite and therefore the higher derivative system is considered to be stable. Afterwards, we derive the consistent interactions in Podolsky's theory within the framework of Hamiltonian BRST-invariant deformation procedure. The key ingredients in our analysis are the local BRST-cohomology which plays a crucial role in the determination of the first-order deformation as well as the Jacobi identity that will greatly simplify the calculations for us. We assert that in our discussions, the second-order deformation and the other higher order deformations of the BRST charge naturally turn out to be zero while the third-order as well as the corresponding higher order BRST-invariant Hamiltonian deformations also vanish completely. Moreover, we evaluate the path integral of the higher derivative constrained system before and after deformation process following the standard BRST quantization method with appropriate gauge-fixing fermions.

我们通过构造一系列 2 参数有界守恒量来研究 Podolsky 广义电动力学中的稳定性问题。通过这种方式，我们表明能量-动量张量的 00 分量可以是正定的，因此高阶导数系统被认为是稳定的。之后，我们在哈密顿 BRST 不变变形过程的框架内推导出 Podolsky 理论中的一致相互作用。我们分析中的关键成分是局部 BRST 上同调，它在确定一阶变形以及雅可比恒等式中起着至关重要的作用，这将大大简化我们的计算。我们断言，在我们的讨论中，BRST 电荷的二阶变形和其他高阶变形自然变成零，而三阶以及相应的高阶 BRST 不变哈密顿变形也完全消失。此外，我们按照标准 BRST 量化方法和适当的规范固定费米子，在变形过程之前和之后评估高导数约束系统的路径积分。