All Physics Faculty Publications

Quanta Without Quantization

Document Type


Journal/Book Title/Conference

Quanta without Quantization

Publication Date



The dimensional properties of fields in classical general relativity lead to a tangent tower structure which gives rise directly to quantum mechanical and quantum field theory structures without quantization.

We derive all the fundamental elements of quantum mechanics from the tangent tower structure, including fundamental commutation relations, a Hilbert space of pure and mixed states, measurable expectation values, Schrödinger time evolution, "collapse" of a state and the probability interpretation.

The most central elements of string theory also follow, including an operator valued mode expansion like that in string theory as well as the Virasoro algebra with central charges.


Available at:

This document is currently not available here.