Richard P. Feynman proposes a new notation for handling operators in quantum mechanics, which allows for easier manipulation of complex expressions involving noncommuting operators. The new notation uses subscripts to indicate the order of operation, such as $A_s B_s$, where the subscript $s$ can be interpreted as a coordinate variable. This approach simplifies the handling of operator functions and allows for the application of ordinary analysis techniques. Feynman discusses the theory of operators in an appendix and provides illustrative applications to quantum mechanics. He also applies the new notation to quantum electrodynamics, showing how it can be used to understand the interrelations between different theoretical formulations. The paper includes a discussion of the Dirac equation and the interpretation of the operator ordering parameter. Finally, it provides a summary of numerical constants appearing in formulas for transition probabilities.Richard P. Feynman proposes a new notation for handling operators in quantum mechanics, which allows for easier manipulation of complex expressions involving noncommuting operators. The new notation uses subscripts to indicate the order of operation, such as $A_s B_s$, where the subscript $s$ can be interpreted as a coordinate variable. This approach simplifies the handling of operator functions and allows for the application of ordinary analysis techniques. Feynman discusses the theory of operators in an appendix and provides illustrative applications to quantum mechanics. He also applies the new notation to quantum electrodynamics, showing how it can be used to understand the interrelations between different theoretical formulations. The paper includes a discussion of the Dirac equation and the interpretation of the operator ordering parameter. Finally, it provides a summary of numerical constants appearing in formulas for transition probabilities.