In this work, we provide a detailed derivation of Foldy-Wouthuysen (FW) transformation for two-dimensional (2D) gapped Dirac fermions under external fields and apply the formalism to study valley excitons in 2D semiconducting materials. Similar to relativistic quantum few-body problem, the gapped Dirac equation can be transformed into a Schr{o}dinger equation with relativistic correction terms. In this 2D materials system, the correction terms can be interpreted as the Berry-curvature effect. The Hamiltonian for a valley exciton in external fields can be written based on the FW transformed Dirac Hamiltonian. Various valley-dependent effects on excitons, such as fine-structure splittings of exciton energy levels, valley-selected exciton transitions, and exciton valley Zeeman effect are discussed within this framework.
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