Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
Pavel Yu. Moshin, Alexander A. Reshetnyak
备注：
64 pages, no figures, notes on functional integral, superdeterminants, Eq.(5.30), Ward identities for SM in GZ form (5.43)-(5.45) added, Discussions extended by Proposition 7 and related formulae, Eq.(5.43)-(5.45) corrected, remarks on gauge-invariant regularization, renormalization added, 14 references added, misprints corrected
我们继续我们的研究Nucl.Phys B888，92（2014）; Int.J.Mod.Phys.A29，1450159（2014）; Phys. Lett. B739，110（2014）; Int.J.Mod.Phys.A30，1550021（2015），并扩展了具有奇值参数$λ_{a}$、$a=1,2$的有限BRST-antiBRST变换类，这些参数在这些作品中引入。在这样做时，我们评估的雅可比诱导有限的BRST-antiBRST变换线性的功能依赖的参数，以及那些诱导有限的BRST-antiBRST变换与任意功能参数。计算涵盖了具有闭代数的规范理论、具有第一类约束的动力系统和一般规范理论的情况。在线性化变换的情况下，所得到的雅可比矩阵不同于多项式依赖于参数的情况下的雅可比矩阵。具有任意参数的有限BRST-反BRST变换会对量子作用产生额外的贡献，而这种贡献不能被吸收到规范的变化中。这些变换包括一个扩展的情况下，功能相关的参数，这意味着一个修改后的补偿方程，承认非平凡的解决方案，导致雅可比等于单位。将含函数依赖参数的有限BRST-antiBRST变换应用于标准模型，得到了函数依赖参数$λ_{a}$的显式形式，证明了路径积分在任何$3$参数$R_{\boldsymbolξ}$类规范中的等价性.将Gribov-Zwanziger理论推广到标准模型的情形，并提出了朗道规范和$R_{\boldsymbolξ}$类规范中Gribov视界泛函的一种形式，其中Gribov视界泛函采用了与场相关的BRST-反BRST变换，并采用了与规范无关的方式，而Gribov视界泛函则采用了与横截类似的非阿贝尔规范场，并在类$R_{\boldsymbolξ}$规范中提出了Gribov视界泛函的一种形式.
英文摘要：
We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters $λ_{a}$, $a=1,2$, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters $λ_{a}$ is obtained, providing the equivalence of path integrals in any $3$-parameter $R_{\boldsymbolξ}$-like gauges. The Gribov--Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in $R_{\boldsymbolξ}$-like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in $R_{\boldsymbolξ}$-like gauges using transverse-like non-Abelian gauge fields.
