Δ + = − 2 ξP $^{+}$; ˜ F αβ ≡ 1 $_{2}$ϵ $^{αβγδ}$F$_{γδ}$ is the dual gluon field strength. Throughout this paper we adopt the light-cone gauge A + = 0, so that the gauge link does not appear in the operators in definitions (2), (3). The definition (2) differs from other definitions encountered in the literature (see [4]). For 0 ≤ x ≤ 1: The same relations hold for E g and ˜ E g respectively. As the gluon itself is its own antiparticle gluon GPDs H $^{g}$( x, ξ, t ), E $^{g}$( x, ξ, t ) defined in (2) are even functions of x : Gluon GPDs ˜ H $^{g}$( x, ξ, t ), ˜ E $^{g}$( x, ξ, t ) defined in (3) are odd functions of x : Let us stress that in what follows we consider the gluon GPDs in nucleon (2), (3) on the interval 0 ≤ x ≤ 1. In the froward limit gluon GPDs H g and ˜ H g reduce to usual forward gluon distributions in the nucleon g ( x ) and Δ g ( x ), while GPD E g and ˜ E g are reduced to unknown gluon distributions, which we denote as e $^{g}$( x ) and Δ e $^{g}$( x ): Note that the forward gluon distributions g ( x ), Δ g ( x ) and e $^{g}$( x ), Δ e $^{g}$( x ) are continued to the negative value of their argument according to: 4 g ( x ) = − g ( − x ) ; e $^{g}$( x ) = − e $^{g}$( − x ) ; Δ g ( x ) = Δ g ( − x ) ; Δ e $^{g}$( x ) = Δ e $^{g}$( − x ) . (7) H $^{g}$( x, 0 , 0) = xg ( x ); E $^{g}$( x, 0 , 0) = xe $^{g}$( x ) ; ˜ H $^{g}$( x, 0 , 0) = x Δ g ( x ); ˜ E $^{g}$( x, 0 , 0) = x Δ e $^{g}$( x ) . (6) ˜ H $^{g}$( x, ξ, t ) = − ˜ H $^{g}$( − x, ξ, t ) ; ˜ E $^{g}$( x, ξ, t ) = − ˜ E $^{g}$( − x, ξ, t ) . (5) H $^{g}$( x, ξ, t ) = H $^{g}$( − x, ξ, t ) ; E $^{g}$( x, ξ, t ) = E $^{g}$( − x, ξ, t ) . (4) H $^{g}$( x, ξ, t ) | here = H $^{g}$( x, ξ, t ) | [3] + H $^{g}$( − x, ξ, t ) | [3] = x ( H $^{g}$( x, ξ, t ) | [17] − H $^{g}$( − x, ξ, t ) | [17] ) . ˜ H $^{g}$( x, ξ, t ) | here = ˜ H $^{g}$( x, ξ, t ) | [3] − ˜ H $^{g}$( − x, ξ, t ) | [3] = x ˜ H $^{g}$( x, ξ, t ) | [17] + ˜ H $^{g}$( − x, ξ, t ) | [17] .