these are complex vectors that are used to transform three-dimensional rotations into two-dimensional representations and they later played a fundamental role in quantum mechanics. cartan published the two volume work lecons sur la theorie des spineurs in 1938.

How would the previous sentence be correctly capitalized?
These are complex vectors that are used to transform three-dimensional rotations into two-dimensional representations and they later played a fundamental role in quantum mechanics. Cartan published the two volume work Lecons sur la theorie des spineurs in 1938.