  We investigate the quartet correlations in four-component fermionic systems
at the thermodynamic limit within a variational many-body theory. The
Bardeen-Cooper-Schrieffer (BCS)-type variational wave function is extended to
the systems with the coexistence of pair and quartet correlations at zero
temperature. Special attention is paid to the application of the present
framework to an alpha-particle condensation in symmetric nuclear matter, where
the coexistence of deuteron and alpha condensations is anticipated. We also
discuss how physical properties, such as quasiparticle dispersion, can be
modified by the pair and quartet correlations and show a hierarchical structure
of in-medium cluster formations in infinite nuclear matter. The present results
may also contribute to the interdisciplinary understanding of fermionic
condensations beyond the BCS paradigm in many-body systems.
