In grammar, the term "first person" refers to a writing style in which the author speaks for or about himself. First-person singular pronouns are "I," "me" and "my." First-person plural pronouns are "we," "us" and "ours." If you are the sole author of an academic paper, it is acceptable to use the first-person singular. If there are multiple authors, the authors as a group may be referred to using the first-person plural.
The first person plural may not be used to refer to society, a particular group of people such as psychologists, or humankind as a whole. For example, "We rely on behavioral observations ...." It is unclear who or what "we" refers to. You must disambiguate these constructions: "Behavioral psychologists rely on behavioral observations ...."
Sometimes authors will use the third person ("he," "she," "they," etc.) because the tone sounds more objective and professional. In doing so, the authors refer to themselves in their writing as "the authors" or "the researchers" instead of as "we." This can also lead to ambiguities. Consider the following example.
"Smith (2002) and Doe and Roe (2004) both noted a correlation between variable X and variable Y. The authors build on these findings in a series of four experiments."
In this passage, "the authors" is ambiguous. It is unclear whether it refers to Smith, Doe and Roe, or to the authors of the current paper.
The first person must not be overused. It can give the paper a tone of narcissism and self-importance. It is vital to keep the paper focused on the research it self. Instead of saying, "We have shown that ...," it is better to say, "The results of the study have shown that...." But be careful of anthromorphizing the work. "An experiment" cannot control for variables, for example, but "the authors" or "we" can.
Consult the APA manual for its full guidelines on writing abstracts. The sixth edition's section on abstracts sets forth no rules about points-of-view.