Timeline for Wick ordering, probability vs physics
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26 at 16:30 | comment | added | CBBAM | @CarloBeenakker Assuming my understanding is correct, then as a follow up how would one define Wick ordering for operators that are not multiplication operators, where integration against the probability measure isn't well-defined? | |
| Apr 26 at 16:30 | comment | added | CBBAM | @CarloBeenakker Thank you. With this insight what I understand so far is the purpose of Wick ordering is to redefine polynomials so that they are orthogonal with respect to a Hamiltonian dependent probability measure. This is done by either the recursive definition above or equivalently using Hermite polynomials (both of which agree with the physicist's idea of "move all creation operators to the left and annihilation operators to the right"). This orthogonality is important since without it we would not get vanishing vacuum expectation values. | |
| Apr 26 at 15:56 | comment | added | Carlo Beenakker | indeed, that is how I understand it. | |
| Apr 26 at 15:52 | comment | added | CBBAM | @CarloBeenakker Thank you, so in probabilistic terms this would mean the Wick ordering depends on the probability measure (where the probability measure is defined using the ground state of the Hamiltonian)? | |
| Apr 26 at 9:22 | comment | added | Carlo Beenakker | one thing to keep in mind, when considering different definitions of Wick ordering: the ordering is defined relative to a vacuum state (ground state of a Hamiltonian), which is the state that is implicit in the equation $\langle :X_1\ldots X_n:\rangle = 0$; a different vacuum state will produce a different Wick ordering; this applies to the physics context when there is superconducting pairing; then the prescription "move all creation operators to the left and annihilation operators to the right" has to be changed. | |
| Apr 26 at 3:30 | history | asked | CBBAM | CC BY-SA 4.0 |