Quantum-invariant theory and the evolution of a quantum scalar field in Robertson-Walker flat spacetimes

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Abstract
On the basis of the generalized invariant formulation, the invariant-related unitary transformation method is developed and used to study the evolution of a quantum scalar field in Robertson-Walker flat spacetimes. We first solve the functional Schrödinger equation for a free scalar field and obtain the exact solutions, of which the ground-state solution possesses isotropy and homogeneity automatically. We then investigate a way of extending the method to treat the case in which there is a high-order perturbative self-interaction.