5 research outputs found
Renormalized Poincar\'e algebra for effective particles in quantum field theory
Using an expansion in powers of an infinitesimally small coupling constant
, all generators of the Poincar\'e group in local scalar quantum field
theory with interaction term are expressed in terms of annihilation
and creation operators and that result from a
boost-invariant renormalization group procedure for effective particles. The
group parameter is equal to the momentum-space width of form factors
that appear in vertices of the effective-particle Hamiltonians, . It
is verified for terms order 1, , and , that the calculated generators
satisfy required commutation relations for arbitrary values of .
One-particle eigenstates of are shown to properly transform under
all Poincar\'e transformations. The transformations are obtained by
exponentiating the calculated algebra. From a phenomenological point of view,
this study is a prerequisite to construction of observables such as spin and
angular momentum of hadrons in quantum chromodynamics.Comment: 17 pages, 5 figure
Boost-Invariant Running Couplings in Effective Hamiltonians
We apply a boost-invariant similarity renormalization group procedure to a
light-front Hamiltonian of a scalar field phi of bare mass mu and interaction
term g phi^3 in 6 dimensions using 3rd order perturbative expansion in powers
of the coupling constant g. The initial Hamiltonian is regulated using momentum
dependent factors that approach 1 when a cutoff parameter Delta tends to
infinity. The similarity flow of corresponding effective Hamiltonians is
integrated analytically and two counterterms depending on Delta are obtained in
the initial Hamiltonian: a change in mu and a change of g. In addition, the
interaction vertex requires a Delta-independent counterterm that contains a
boost invariant function of momenta of particles participating in the
interaction. The resulting effective Hamiltonians contain a running coupling
constant that exhibits asymptotic freedom. The evolution of the coupling with
changing width of effective Hamiltonians agrees with results obtained using
Feynman diagrams and dimensional regularization when one identifies the
renormalization scale with the width. The effective light-front Schroedinger
equation is equally valid in a whole class of moving frames of reference
including the infinite momentum frame. Therefore, the calculation described
here provides an interesting pattern one can attempt to follow in the case of
Hamiltonians applicable in particle physics.Comment: 24 pages, LaTeX, included discussion of finite x-dependent
counterterm
Special relativity constraints on the effective constituent theory of hybrids
We consider a simplified constituent model for relativistic
strong-interaction decays of hybrid mesons. The model is constructed using
rules of renormalization group procedure for effective particles in light-front
quantum field theory, which enables us to introduce low-energy phenomenological
parameters. Boost covariance is kinematical and special relativity constraints
are reduced to the requirements of rotational symmetry. For a hybrid meson
decaying into two mesons through dissociation of a constituent gluon into a
quark-anti-quark pair, the simplified constituent model leads to a rotationally
symmetric decay amplitude if the hybrid meson state is made of a constituent
gluon and a quark-anti-quark pair of size several times smaller than the
distance between the gluon and the pair, as if the pair originated from one
gluon in a gluonium state in the same effective theory.Comment: 11 pages, 5 figure
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
Deep Inelastic Structure Functions in Light-Front QCD: Radiative Corrections
Recently, we have introduced a unified theory to deal with perturbative and
non-perturbative QCD contributions to hadronic structure functions in deep
inelastic scattering. This formulation is realized by combining the coordinate
space approach based on light-front current algebra techniques and the momentum
space approach based on Fock space expansion methods in the Hamiltonian
formalism of light-front field theory. In this work we show how a perturbative
analysis in the light-front Hamiltonian formalism leads to the factorization
scheme we have proposed recently. The analysis also shows that the scaling
violations due to perturbative QCD corrections can be rather easily addressed
in this framework by simply replacing the hadron target by dressed parton
target and then carrying out a systematic expansion in the coupling constant
based on the perturbative QCD expansion of the dressed parton
target. The tools employed for this calculation are those available from
light-front old-fashioned perturbation theory. We present the complete set of
calculations of unpolarized and polarized deep inelastic structure functions to
order . We extract the relevant splitting functions in all the cases.
We explicitly verify all the sum rules to order . We demonstrate the
validity of approximations made in the derivation of the new factorization
scheme. This is achieved with the help of detailed calculations of the
evolution of structure function of a composite system carried out using
multi-parton wavefunctions.Comment: Revtex, 26 pages and no figur