What semantic field underlies 經?
The earliest documented meaning of 经 is "to weave". It does not mean that in modern Chinese, but it can still mean warp. 
In weaving, warp is the name for the threads that are fixed into the weaving frame, where fabric is created by pushing the weft through horizontally. 

From the meaning weave, it expanded towards the verbal meanings it has today:  


To order or operate as in the modern words 经营 or 经理  
To pass through or experience as in the modern words 经历 or 经过. From here it expanded to mean constant, regular as in 经常, and things that are constant like the 经书 (canonical scriptures).




From the meaning warp, 经 expanded to mean "vertical" lines along certain things, such as the "energy channels" in a human body or the longitudinal lines on planet earth.

The meaning "canonical scriptures" can also be derived from the warp meaning, because these are the books that span "vertically" through time, whereas later commentaries are woven through "horizontally". 



So the underlying image is always that of a weaving frame. But some of the modern / later meanings have moved very far from that original meaning. I don't think there is one semantic field that comfortably contains all of 经's various meanings.