# Definition of the Effective Particle

We define the effective particle creation and annihilation operators which are collectively and commonly denoted by $\hat{q}_s$:

$$\hat{q}_s := \hat{U}_s \, \hat{q}_0 \, \hat{U}^\dagger_s$$

where $s$ is a renormalization group parameter, $0< s < \infty$, $\hat{U}_s$ is an unitary operator and $\hat{q}_0$ collectively and commonly denotes the creation and annihilation operators in our familiar canonical theory. Due to the values of $s$, for each bare particle/particles state we get a family of effective particle/particles states. The particles associated with the effective particle/particles states are called the effective particles.

My question: Is $\hat{U}_s$ is a function of $\hat{q}_0$; i.e., $\hat{U}_s (\hat{q}_0)$ ?

• Do you have a reference that would help to understand the context of your question ? – Adam May 10 '14 at 22:25
• Simply google: PERTURBATIVE FORMULAE FOR RELATIVISTIC INTERACTIONS OF EFFECTIVE PARTICLES by Stanisław D. Głazek – omehoque May 11 '14 at 8:59