44 research outputs found
Limit cycles of effective theories
A simple example is used to show that renormalization group limit cycles of
effective quantum theories can be studied in a new way. The method is based on
the similarity renormalization group procedure for Hamiltonians. The example
contains a logarithmic ultraviolet divergence that is generated by both real
and imaginary parts of the Hamiltonian matrix elements. Discussion of the
example includes a connection between asymptotic freedom with one scale of
bound states and the limit cycle with an entire hierarchy of bound states.Comment: 8 pages, 3 figures, revtex
Large-momentum convergence of Hamiltonian bound-state dynamics of effective fermions in quantum field theory
Contributions to the bound-state dynamics of fermions in local quantum field
theory from the region of large relative momenta of the constituent particles,
are studied and compared in two different approaches. The first approach is
conventionally developed in terms of bare fermions, a Tamm-Dancoff truncation
on the particle number, and a momentum-space cutoff that requires counterterms
in the Fock-space Hamiltonian. The second approach to the same theory deals
with bound states of effective fermions, the latter being derived from a
suitable renormalization group procedure. An example of two-fermion bound
states in Yukawa theory, quantized in the light-front form of dynamics, is
discussed in detail. The large-momentum region leads to a buildup of
overlapping divergences in the bare Tamm-Dancoff approach, while the effective
two-fermion dynamics is little influenced by the large-momentum region. This is
illustrated by numerical estimates of the large-momentum contributions for
coupling constants on the order of between 0.01 and 1, which is relevant for
quarks.Comment: 22 pages, 9 figure
Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model
A continuous sequence of infinitesimal unitary transformations, combined with
an operator product expansion for vertex operators, is used to diagonalize the
quantum sine-Gordon model for 2 pi < beta^2 < infinity. The leading order of
this approximation already gives very accurate results for the single-particle
gap in the strong-coupling phase. This approach can be understood as an
extension of perturbative scaling theory since it links weak to strong-coupling
behavior in a systematic expansion. The approach should also be useful for
other strong-coupling problems that can be formulated in terms of vertex
operators.Comment: 4 pages, 1 figure, minor changes (typo in Eq. (3) corrected,
references added), published versio
Neutrino oscillations in the front form of Hamiltonian dynamics
Since future, precise theory of neutrino oscillations should include the
understanding of the neutrino mass generation and a precise, relativistic
description of hadrons, and observing that such a future theory may require
Dirac's FF of Hamiltonian dynamics, we provide a preliminary FF description of
neutrino oscillations using the Feynman--Gell-Mann-Levy version of an effective
theory in which leptons interact directly with whole nucleons and pions,
instead of with quarks via intermediate bosons. The interactions are treated in
the lowest-order perturbative expansion in the coupling constants in the
effective theory, including a perturbative solution of the coupled constraint
equations. Despite missing quarks and their binding mechanism, the effective
Hamiltonian description is sufficiently precise for showing that the standard
oscillation formula results from the interference of amplitudes with different
neutrinos in virtual intermediate states. This holds provided that the inherent
experimental uncertainties of preparing beams of incoming and measuring rates
of production of outgoing particles are large enough for all of the different
neutrino intermediate states to contribute as alternative virtual paths through
which the long-baseline scattering process can manifest itself. The result that
an approximate, effective FF theory reproduces the standard oscillation formula
at the level of transition rates for currently considered long-baseline
experiments--even though the space-time development of scattering is traced
differently and the relevant interaction Hamiltonians are constructed
differently than in the commonly used IF of dynamics--has two implications. It
shows that the common interpretation of experimental results is not the only
one, and it opens the possibility of considering more precise theories taking
advantage of the features of the FF that are not available in the IF.Comment: revtex4, 10 page
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
Neutrino oscillations in the formal theory of scattering
Scattering theory in the Gell-Mann and Goldberger formulation is slightly
extended to render a Hamiltonian quantum mechanical description of the neutrino
oscillations.Comment: revtex4, 4 page
Renormalization approach to many-particle systems
This paper presents a renormalization approach to many-particle systems. By
starting from a bare Hamiltonian with an
unperturbed part and a perturbation ,we define an
effective Hamiltonian which has a band-diagonal shape with respect to the
eigenbasis of . This means that all transition matrix elements are
suppressed which have energy differences larger than a given cutoff
that is smaller than the cutoff of the original Hamiltonian. This
property resembles a recent flow equation approach on the basis of continuous
unitary transformations. For demonstration of the method we discuss an exact
solvable model, as well as the Anderson-lattice model where the well-known
quasiparticle behavior of heavy fermions is derived.Comment: 11 pages, final version, to be published in Phys. Rev.
Color van der Waals forces between heavy quarkonia in effective QCD
The perturbative renormalization group for light-front QCD Hamiltonian
produces a logarithmically rising interquark potential already in second order,
when all gluons are neglected. There is a question if this approach produces
also color van der Waals forces between heavy quarkonia and of what kind. This
article shows that such forces do exist and estimates their strength, with the
result that they are on the border of exclusion in naive approach, while more
advanced calculation is possible in QCD.Comment: 7 pages, elsart, bibliography in .bbl file, to be submitted to
Physics Letters
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
Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
Hamiltonian light-front field theory can be used to solve for hadron states
in QCD. To this end, a method has been developed for systematic renormalization
of Hamiltonian light-front field theories, with the hope of applying the method
to QCD. It assumed massless particles, so its immediate application to QCD is
limited to gluon states or states where quark masses can be neglected. This
paper builds on the previous work by including particle masses
non-perturbatively, which is necessary for a full treatment of QCD. We show
that several subtle new issues are encountered when including masses
non-perturbatively. The method with masses is algebraically and conceptually
more difficult; however, we focus on how the methods differ. We demonstrate the
method using massive phi^3 theory in 5+1 dimensions, which has important
similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra
disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final
published versio