Electron phonon interaction hamiltonian problem

[phdojg]

Hi

In almost every reference I have found the phonon part of the frohlich electron phonon interaction hamiltonian is given by
(b_{q}+b^{\dag}_{-q})

notice the +, where b_{q} is a phonon creation operator and b^{\dag}_{-q})is the destruction operator of a phonon.

however in a paper on colossal magnetoresistance and in the book polarons in advanced materials p69, this + is replaced with a -, I simply cannot understand why this is. There are no real changes to the rest of the hamiltonian simply different constants at the start depending what has been incorperated into the coupling constant. Does anyone have any sugestions as to how or why the sign is different? any sugestions would be really helpful

Many thanks

 

[olgranpappy]

Hi

In almost every reference I have found the phonon part of the frohlich electron phonon interaction hamiltonian is given by
(b_{q}+b^{\dag}_{-q})

notice the +, where b_{q} is a phonon creation operator and b^{\dag}_{-q})is the destruction operator of a phonon.

however in a paper on colossal magnetoresistance and in the book polarons in advanced materials p69, this + is replaced with a -, I simply cannot understand why this is. There are no real changes to the rest of the hamiltonian simply different constants at the start depending what has been incorperated into the coupling constant. Does anyone have any sugestions as to how or why the sign is different? any sugestions would be really helpful

Many thanks

typo maybe? or different definitions of 'b'. Or maybe in one case they interchange a position operator with a momentum operator--e.g., inside a dipole matrix element?

 

[kanato]

Are there any fermion terms? Maybe the minus sign comes from commuting them somewhere in the derivation.