I have never analyzed a Wien Bridge oscillator until now and I have never read one of the thousands of explanations about it on the internet, but here is what I see:
1) R1, R2, C1 and C2 form a bandpass filter that peaks at one frequency and applies positive feedback to the opamp to cause oscillation.
2) R3, R4 and the Jfet provide negative feedback so that the gain is about 3 times. If the gain is less than 3 times then it does not oscillate because I guess the bandpass filter has a loss of 3 times. If the gain is more than 3 times then the output signal level keeps increasing until the opamp has clipping.
3) The diode rectifies the output signal and C5 filters it into a negative DC voltage that is almost the peak voltage of the output signal.
4) The rectified signal's DC voltage decreases or increases the conduction of the Jfet to set the output level.
Look at one of the thousands of explanations in Google and reply about any difference from what I said.