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with 

where the arbitrary function G ( a$_{i}$, p$_{i}$, η ) is expressed as an expansion in terms of the WZ field, given by 

where 

and satisfies the following boundary condition 

The symplectic variables were extended to also encom- pass the WZ variable ˜ ξ (0) ˜ θ = ( ξ (0) $^{θ}$, η ) (with ˜ θ = 1 , 2 , . . . , 2 N + 1) and the first-iterative symplectic poten- tial becomes 

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In this context, the new canonical momenta are 

and the new symplectic tensor is given by 

that is 

To sum up, basically, we have two steps: the first one is addressed to compute Ψ( a$_{i}$, p$_{i}$ ) while the second one 

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is dedicated to the calculation of G ( a$_{i}$, p$_{i}$, η ). In order to begin with the first step, we impose that this new symplectic tensor ( ˜ f $^{(0)}$) has a zero-mode ˜ ν , consequently, we obtain the following condition 

At this point, f becomes degenerated and in consequence, we introduce an obstruction to solve the Hamiltonian equation of motion given by equation (2.8). Assuming that the zero-mode ˜ ν (0) ˜ θ is 

and using the relation given in (2.17) together with (2.16), we have a system of equations, 

where 

The matrix elements µ θ are chosen in order to disclose the desired gauge symmetry. Note that in this formal- ism the zero-mode ˜ ν (0) ˜ θ is the gauge symmetry genera- tor. It is worth to mention that this feature is impor- tant because it opens up the possibility to disclose the desired hidden gauge symmetry from the noninvariant model. From relation (2.17) some differential equations involving Ψ( a$_{i}$, p$_{i}$ ) are obtained, i. e., the equation (2.19), and after a straightforward computation, Ψ( a$_{i}$, p$_{i}$ ) can be determined. 

In order to compute G ( a$_{i}$, p$_{i}$, η ) following the second step of the method, it is mandatory that no constraints arise from the contraction of the zero-mode (˜ ν (0) ˜ $^{θ}$) with the gradient of the potential ˜ V $^{(0)}$( a$_{i}$, p$_{i}$, η ). This condi- tion generates a general differential equation, which reads as 

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that allows us to compute all the correction terms G ( n $^{)}$( a$_{i}$, p$_{i}$, η ) as functions of η . Notice that this poly- nomial expansion in terms of η is equal to zero. Conse- quently, all the coefficients for each order in η must be 

identically null. Given this, each correction term as func- tion of η is determined. For a linear correction term, we 

