论文标题
协方差形式主义中局部仪表转换的noether电流和发电机
Noether currents and generators of local gauge transformations in the covariant canonical formalism
论文作者
论文摘要
我们研究了协变规形式主义（CCF）中局部转换的发生器。 CCF将差分形式视为基本变量的平等基础上的空间和时间。 The conjugate forms $π_A$ are defined as derivatives of the Lagrangian $d$-form $L(ψ^A, dψ^A)$ with respect to $dψ^A$, namely $π_A := \partial L/\partial dψ^A$, where $ψ^A $ are $p$-form dynamical fields.形式的典型方程是从拉格朗日形式的form-legendre变换衍生而来的。我们表明，如果Lagrangian形式的转换由$Δl= dl $和$Δψ^a $和$ l $仅取决于$ψ^a $和参数。例如，我们研究了量规场的局部仪表转换和重力二阶形式的局部洛伦兹变换。
We investigate generators of local transformations in the covariant canonical formalism (CCF). The CCF treats space and time on an equal footing regarding the differential forms as the basic variables. The conjugate forms $π_A$ are defined as derivatives of the Lagrangian $d$-form $L(ψ^A, dψ^A)$ with respect to $dψ^A$, namely $π_A := \partial L/\partial dψ^A$, where $ψ^A $ are $p$-form dynamical fields. The form-canonical equations are derived from the form-Legendre transformation of the Lagrangian form $H:=dψ^A \wedge π_A - L$. We show that the Noether current form is the generator of an infinitesimal transformation $ψ^A \to ψ^A + δψ^A$ if the transformation of the Lagrangian form is given by $δL=dl$ and $δψ^A$ and $l$ depend on only $ψ^A$ and the parameters. As an instance, we study the local gauge transformation for the gauge field and the local Lorentz transformation for the second order formalism of gravity.
