  The exchange of knowledge across different areas and disciplines plays a key
role in the process of knowledge creation, and can stimulate innovation and the
emergence of new fields. We develop here a quantitative framework to extract
significant dependencies among scientific disciplines and turn them into a
time-varying network whose nodes are the different fields, while the weighted
links represent the flow of knowledge from one field to another at a given
period of time. Drawing on a comprehensive data set on scientific production in
modern physics and on the patterns of citations between articles published in
the various fields in the last thirty years, we are then able to map, over
time, how the ideas developed in a given field in a certain time period have
influenced later discoveries in the same field or in other fields. The analysis
of knowledge flows internal to each field displays a remarkable variety of
temporal behaviours, with some fields of physics showing to be more
self-referential than others. The temporal networks of knowledge exchanges
across fields reveal cases of one field continuously absorbing knowledge from
another field in the entire observed period, pairs of fields mutually
influencing each other, but also cases of evolution from absorbing to mutual or
even to back-nurture behaviors.
