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Title: Nonperturbative light-front Hamiltonian methods

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Progress in Particle and Nuclear Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 04:01:06; Journal ID: ISSN 0146-6410
Country of Publication:
United Kingdom

Citation Formats

Hiller, J. R.. Nonperturbative light-front Hamiltonian methods. United Kingdom: N. p., 2016. Web. doi:10.1016/j.ppnp.2016.06.002.
Hiller, J. R.. Nonperturbative light-front Hamiltonian methods. United Kingdom. doi:10.1016/j.ppnp.2016.06.002.
Hiller, J. R.. 2016. "Nonperturbative light-front Hamiltonian methods". United Kingdom. doi:10.1016/j.ppnp.2016.06.002.
title = {Nonperturbative light-front Hamiltonian methods},
author = {Hiller, J. R.},
abstractNote = {},
doi = {10.1016/j.ppnp.2016.06.002},
journal = {Progress in Particle and Nuclear Physics},
number = C,
volume = 90,
place = {United Kingdom},
year = 2016,
month = 9

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Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.ppnp.2016.06.002

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Cited by: 3works
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  • The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar λφ{sup 4} field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.
  • The determination of low-energy bound states in quantum chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve quantum electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling nevermore » leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the constituent quark model with the complexities of quantum chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.« less
  • The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective couplingmore » $$\alpha_s^{AdS}(Q^2)$$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $$ \sim 1$$ GeV. The resulting $$\beta$$-function appears to capture the essential characteristics of the full $$\beta$$-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $$\alpha_s^{AdS}(Q^2)$$.« less
  • In the light-front form of field theory, boost invariance is a manifest symmetry. On the down side, parity and rotational invariance are not manifest, leaving the possibility that approximations or incorrect renormalization might lead to violations of these symmetries for physical observables. In this paper, it is discussed how one can turn this deficiency into an advantage and utilize parity violations (or the absence thereof) in practice for constraining effective light-front Hamiltonians. More precisely, we will identify observables that are both sensitive to parity violations and easily calculable numerically in a nonperturbative framework and we will use these observables tomore » constrain the finite part of noncovariant counterterms in effective light-front Hamiltonians. {copyright} {ital 1996 The American Physical Society.}« less
  • The three-dimensional real scalar model, in which the Z{sub 2} symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal ({phi}{sup 6}) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as {phi}(x){r_arrow}{var_phi}(x)+v. The shifted value v is determined as a function of running mass and coupling so that the mass of the ground state vanishes. {copyright} {ital 1997} {ital The American Physical Society}