In p.8 of Michio Kaku book Introduction to Superstrings and M-Theory-Springer (1998), he said
The gravitational force. Gravity research was totally uncoupled from research in the other interactions. Classical relativists continued to find more and more classical solutions in isolation from particle research. Attempts to canonically quantize the theory were frustrated by the presence of the tremendous redundancy of the theory. There was also the discouraging realization that even if the theory could be successfully quantized, it WOULD ... still be nonrenormalizable.
My question is that
- what does Kaku mean for nonrenormalizable but quantizable theory?
what are the criteria to be nonrenormalizable?
what are the criteria to be quantizable?
- What are examples of nonrenormalizable but quantizable theories?
Fermi weak interaction theory? Gravity? and how come?