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Stanislaw D. Glazek

Publications and source records attributed to Stanislaw D. Glazek.

At least 37 records · Page 2Linked to original sources
arXiv2010

Non-local structure of renormalized Hamiltonian densities on the light-front hyperplane in space-time

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the arbitrary parameter of scale, which characterizes the size of effective particles in terms of the allowed range of virtual energy changes caused by interactions. This article describes a generic example of the non-locality that characterizes light-front interaction Hamiltonian densities of first-order in an effective coupling constant. The same non-locality is also related to a relative motion wave function for a bound state of two particles.

hep-th↗
arXiv2008

Renormalization group and bound states

Renormalization group procedure suggests that the low-energy behavior of effective coupling constant in asymptotically free Hamiltonians is connected with the existence of bound states and depends on how the interactions responsible for the binding are included in the renormalization group equations.

hep-th↗
arXiv2008

Renormalization group and bound states

Similarity renormalization group procedure identifies the role of bound states in the low-energy rate of change of effective coupling constant in a model Hamiltonian with asymptotic freedom.

hep-th↗
arXiv2008

Heuristic model of teaching

A simple physical model differentiates effective from ineffective teaching and identifies elements that make teaching productive, with specific implications concerning training of teachers.

physics.ed-ph↗
arXiv2008

The impact of bound states on similarity renormalization group transformations

We study a simple class of unitary renormalization group transformations governed by a parameter f in the range [0,1]. For f=0, the transformation is one introduced by Wegner in condensed matter physics, and for f=1 it is a simpler transformation that is being used in nuclear theory. The transformation with f=0 diagonalizes the Hamiltonian but in the transformations with f near 1 divergent couplings arise as bound state thresholds emerge. To illustrate and diagnose this behavior, we numerically study Hamiltonian flows in two simple models with bound states: one with asymptotic freedom and a related one with a limit cycle. The f=0 transformation places bound-state eigenvalues on the diagonal at their natural scale, after which the bound states decouple from the dynamics at much smaller momentum scales. At the other extreme, the f=1 transformation tries to move bound-state eigenvalues to the part of the diagonal corresponding to the lowest momentum scales available and inevitably diverges when this scale is taken to zero. We analyze the shift mechanism analytically in a 3x3 matrix model, which displays the essense of this RG behavior.

nucl-th↗
arXiv2007

Heavy Quarkonia in Light-Front QCD

This talk is based on results obtained for masses and wave functions of heavy quarkonia in a light-front Hamiltonian formulation of QCD with just one flavor of quarks using an ansatz for the mass-gap for gluons. Since the calculated spectra compare reasonably well with data, some further steps one can make are discussed.

hep-ph↗
arXiv2006

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.

hep-th↗
arXiv2006

Boost-invariant Hamiltonian approach to heavy quarkonia

Light-front Hamiltonian formulation of QCD with only one flavor of quarks is used in its simplest approximate version to calculate masses and boost-invariant wave functions of c-anti-c or b-anti-b mesons. It is shown that in the Hamiltonian approach in its simplest version the strong coupling constant alpha and quark mass m (for suitable values of the renormalization group parameter lambda that is used in the calculation), can be adjusted so that a) masses of 12 lightest well-established b-anti-b mesons are reproduced with accuracy better than 0.5 percent for all of them, which means 50 MeV in a few worst cases and on the order of 10 MeV in other cases, or b) masses of 11 lightest c-anti-c mesons are reproduced with accuracy better than 3 percent for all of them, which means better than 100 MeV in a few worst cases and on the order of 10 MeV in the other cases, while the parameters alpha and m are near the values expected in the cases a) and b) by analogy with other approaches. A 4th-order study in the same Hamiltonian scheme will be required to explicitly include renormalization group running of the parameters alpha and m from the scale set by masses of bosons W and Z down to the values of lambda that are suitable in the bound-state calculations. In principle, one can use the Hamiltonian approach to describe the structure, decay, production, and scattering of heavy quarkonia in all kinds of motion, including velocities arbitrarily close to the speed of light. This work is devoted exclusively to a pilot study of masses of the quarkonia in the simplest version of the approach.

hep-th↗
arXiv2006

Special relativity in decays of hybrids

A decay of a heavy hybrid is expected to produce light mesons flying out with speeds comparable to the speed of light and phenomenological models of the decay must respect symmetries of special relativity. We study consequences of this requirement in a class of simple constituent models with spin. Our models respect boost symmetry because they conform to the rules of a boost-invariant renormalization group procedure for effective particles in light-front QCD. But rotational symmetry of the decay amplitude is not guaranteed and the parameters in the model wave functions must take special values in order to obtain the symmetry. When the effective interaction Hamiltonian responsible for a hybrid decay has the same structure as the gluon-quark-antiquark interaction term obtained by solving the renormalization group equations for Hamiltonians in first order perturbation theory, the non-relativistic image of a hybrid as built from a quark and an antiquark and a heavy gluon that typically resides between the quarks, cannot produce rotationally symmetric amplitude. However, there exists an alternative generic picture in the model that does satisfy the requirements of special relativity. Namely, the distance between the quark and antiquark must be much smaller than the distance between the gluon and the pair of quarks, as if a hybrid were similar to a gluonium in which one gluon is replaced by a quark-antiquark pair.

hep-ph↗
arXiv2003

Similarity renormalization group as a theory of effective particles

The similarity renormalization group procedure formulated in terms of effective particles is briefly reviewed in a series of selected examples that range from the model matrix estimates of its numerical accuracy to issues of the Poincare symmetry in constituent theories to derivation of the Schroedinger equation for quarkonia in QCD.

hep-th↗
arXiv2003

Accuracy estimate for a relativistic Hamiltonian approach to bound-state problems in theories with asymptotic freedom

Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple enough to study the method up to sixth order in the expansion. The procedure is found in this case to match the precision of the best available benchmark method of the altered Wegner flow equation, reaching the accuracy of a few percent.

hep-th↗
arXiv2003

Harmonic oscillator force between heavy quarks

A renormalization group procedure for effective particles is applied to quantum chromodynamics of one flavor of quarks with large mass m in order to calculate light-front Hamiltonians for heavy quarkonia, H_lambda, using perturbative expansion in the coupling constant alpha_lambda. lambda is the renormalization group parameter with the interpretation of an inverse of the spatial size of the color charge distribution in the effective quarks and gluons. The eigenvalue equation for H_lambda couples quark-anti-quark states with sectors of a larger number of constituents. The coupling to states with more than one effective gluon, and interactions in the quark-anti-quark-gluon sector, are removed at the price of introducing an ansatz for the gluon mass, mu^2. The simplified equation is used to evaluate a new Hamiltonian of order alpha_lambda that acts only in the effective quark-anti-quark sector and in the non-relativistic limit turns out to contain the Coulomb term with Breit-Fermi orrections and spin-independent harmonic oscillator term with frequency omega = [(4/3)(alpha_lambda/pi)]^1/2 lambda (lambda/m)^2 (pi/1152)^1/4. The latter originates from the hole excavated in the overlapping quark self-interaction gluon clouds by the exchange of effective gluons between the quarks. The new term is largely independent of the details of mu^2 and in principle can fit into the ball park of phenomenology. The first approximation can be improved by including more terms in H_lambda and solving the eigenvalue equations numerically.

hep-th↗
arXiv2003

Universality, marginal operators, and limit cycles

The universality of renormalization group limit cycle behavior is illustrated with a simple discrete Hamiltonian model. A non-perturbative renormalization group equation for the model is soluble analytically at criticality and exhibits one marginal operator (made necessary by the limit cycle) and an infinite set of irrelevant operators. Relevant operators are absent. The model exhibits an infinite series of bound state energy eigenvalues. This infinite series approaches an exact geometric series as the eigenvalues approach zero - also a consequence of the limit cycle. Wegner's eigenvalues for irrelevant operators are calculated generically for all choices of parameters in the model. We show that Wegner's eigenvalues are independent of location on the limit cycle, in contrast with Wegner's operators themselves, which vary depending on their location on the limit cycle. An example is then used to illustrate numerically how one can tune the initial Hamiltonian to eliminate the first two irrelevant operators. After tuning, the Hamiltonian's bound state eigenvalues converge much more quickly than otherwise to an exact geometric series.

cond-mat↗
arXiv2002

Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states

A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians, through adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states, with the exact bound state energy in the model. The improved perturbative calculus leads to a few-percent accuracy in a systematic expansion.

hep-th↗
arXiv2002

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.

hep-ph↗
arXiv2002

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.

hep-th↗