content_image/393502.jpg content_image/393503.jpg content_image/393505.jpg content_image/393500.jpg content_image/393504.jpg content_image/393501.jpg content_image/393506.jpg content_image/393507.jpg
the zeroth-iterative symplectic tensor is obtained as 

<img src='content_image/393502.jpg'>

This matrix is obviously singular, thus, it has a zero- mode that generates a constraint when contracted with the gradient of the potential U $^{(0)}$, given by, 

<img src='content_image/393503.jpg'>

that is identified as being the Gauss law, which satisfies the following Poisson algebra, 

Substituting the constraint Ω$_{1}$ into the canonical sec- tor of the first-order Lagrangian through a Lagrange multiplier η , we have the first-iterative Lagrangian L $^{(1)}$, namely, 

<img src='content_image/393505.jpg'>

with the first-order symplectic potential given by 

<img src='content_image/393500.jpg'>

where U = U $^{(0)}$. Therefore, the symplectic variables become ξ (1) α = ( φ, π$_{φ}$, A$_{0}$, A$_{1}$, π$_{1}$, η ) with the following one-form canonical momenta, 

<img src='content_image/393504.jpg'>

The corresponding matrix f (1) is then 

<img src='content_image/393501.jpg'>

<img src='content_image/393506.jpg'>

which is a nonsingular matrix. The inverse of f $^{(1)}$( x, y ) furnishes, after a straightforward calculation, the Dirac brackets among the physical fields, 

<img src='content_image/393507.jpg'>

