I've been looking at the Pierce oscillator and I'm unsure of the role played by the series caps to ground (the so-called pi network).
I've put together an image which attempts to explain my intuition (the 1's and 0's are a simplification; I understand that the crystal produces a sine wave).
I assume the action of the crystal – oscillating back and forth – causes the caps to charge and discharge and, crucially, produce the 180 degree phase shift at the inverter input pin.
The feedback "kick" is produced every half-cycle in response to C1 charging and is in-phase with the crystals current movement during this period.
Incidentally, as I understand it, the large resistor R1 is designed to put the inverter in a highly sensitive state (hovering around Vcc/2) where the slightest tip either way produces a large output (relatively speaking) in the opposite direction. This is possible because an inverter output of Vcc could feed the input, in tiny increments though the feedback resistor, from 0 to just shy of Vcc/2 before it would "flip". Then, of course, it would draw current from the input and so on until finally it settled at a balancing point around Vcc/2.
Is that more-or-less how it is?
Best Answer
Without capacitors how can you expect the crystal to produce a phase shift of 180 degrees at its resonance. There needs to be 180 degrees of phase shift because you need a total of 360 degrees and the inverter provides only 180 degrees hence it's called an inverter.
If you want to read more try this - it's quite a good document on the subject by Microchip entitled AN826 Crystal oscillator basics.
Here is also a very good article about figuring out the series resonant point and the parallel resonant point (all xtals have them and this basically determines the capacitor values chosen.