  We outline a method of deriving boost invariant hamiltonians for effective
particles in quantum field theory. The hamiltonians are defined and calculated
using creation and annihilation operators in light-front dynamics. The
renormalization group equations are written for a sequence of unitary
transformations which gradually transform the bare canonical creation and
annihilation operators of a local theory to the creation and annihilation
operators of effective particles in an effective theory with the same dynamical
content but a finite range of energy transfers due to form factors in the
interaction vertices. The boost invariant effective hamiltonians can be used to
describe the constituent dynamics in relativistically moving systems including
the rest and the infinite momentum frame. The general equations are illustrated
in perturbation theory by second-order calculations of self-energy and
two-particle interaction terms in Yukawa theory, QED and QCD. In Yukawa theory,
one obtains the generalized Yukawa potential including its full
off-energy-shell extension and form factors in the vertices. In QED, the
effective hamiltonian eigenvalue problem converges for small coupling constants
to the Schr\"odinger equation but the typical relativistic ultraviolet
singularities at short distances between constituents are regularized by the
similarity form factors. In the second-order QCD effective hamiltonian one
obtains a boost invariant logarithmically confining quark-anti-quark
interaction term which may remain uncanceled in the non-abelian dynamics of
effective quarks and gluons.
