Posted:

**Oct 06, 2011 8:13 pm**Teuton wrote:twistor59 wrote:

Edit: after seeing Teuton's response, I should clarify that I'm talking about a quantum field, not a generic field. There are also people who define quantum fields in Teutonic language

What is the essential physical difference between "classical" fields and quantum fields?

A classical field assigns a value of some measurable quantity to each point in spacetime.

A quantum field assigns an operator to each point in spacetime (this is the heuristic version - the more mathematically rigorous version involves operator valued distributions as I alluded to earlier). This operator acts on "states" which live in an abstract (Hilbert) space and does stuff like changing the number of quanta.