The paper is concerned with the Cauchy problem for the Dirac-Klein-Gordon equations
with initial data
Here, is a two-spinor field, and is real-valued, , with Hermitian -matrices satisfying , , .
The main result states that (1)–(3) is globally well-posed for initial data , , . The solution satisfies , , . A second theorem deals with more regular initial data , , for . In the case of smooth data, there exists a global smooth classical solution.