We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

中文翻译：

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一阶形式中波多尔斯基广义电动力学的典型哈密顿分析

我们通过引入两组新变量来对波多尔斯基的广义电动力学进行规范哈密顿分析，这有助于我们将拉格朗日方程转换为等效的一阶形式。剔除非物理扇区后，计算高阶导数系统的物理自由度，得到约化相空间中的狄拉克括号。然后借助第一类约束，我们构造了与BRST电荷和BRST不变哈密顿量密切相关的独立规范发生器。最后，通过选择合适的规范固定费米子，我们在广义Lorenz规范条件下评估了BRST量化方案中这个更高导数约束系统的路径积分。