The wave-particle description of quantum mechanics is briefly reviewed to set an analogy between the quantum mechanics of particles and fields and quantum cosmology. It is shown that quantum cosmology can be seen as a quantum field theory developed in the space of three metrics (the metrics of the spatial sections of the spacetime), where the classical evolution of the universe corresponds to a definite trajectory and the quantum mechanics of matter fields emerges as the first order quantum correction. Like in a quantum field theory developed in an isotropic background, the universes are created in universe-antiuniverse pairs, which might provide us with an explanation for the matter-antimatter asymmetry observed in our universe without going beyond the standard model. Moreover, the states of the matter and the antimatter fields of the pair of universes are entangled and that makes that their initial states are in a non-vacuum state (presumably in a thermal state). That might open the possibility of looking for observable imprints of the creation of universes in pairs is the astronomical data.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).