Physics Education Research has for a long time primarily been concerned with helping students to learn physics and to "think like a physicist." This paper explores the emerging subfield where students' identity development is analyzed to examine processes of "becoming a physicist" in a wider sense. Drawing on sociocultural theories and methodologies, and specifically analyzing identity and discourse, I focus on what happens when students with differing outlooks on physics encounter advanced physics courses. A discourse analytical framework allows one to inquire into the messages about "who one should be as a physicist" communicated to students during courses. This enables a discussion of what physicist identities are made possible for physics students. In this way, a discourse perspective can be one way of analyzing identities in physics without taking the norms of the discipline for granted.