Quarkonia in Hamiltonian Light-Front QCD

Brisudová, Martina M.; Perry, Robert J.; Wilson, Kenneth G.

doi:10.1103/physrevlett.78.1227

Cited by 64 publications

(62 citation statements)

References 8 publications

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“…McCartor and Dalley [190] have derived an effective Hamiltonian operator to induce chiral symmetry breaking; this could be incorporated into a study of mesons in QCD. There is also a construction of a confining interaction based on the requirement of restoration for rotational symmetry [191,192,193].…”

Section: Quantum Chromodynamicsmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

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Section: Quantum Chromodynamicsmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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“…They are therefore unlikely to violate fundamental symmetries like gauge and Lorentz-invariance. Usually one proceeds in the reverse order [15,16,17,18,19,26,31,32,34,35]: One first truncates and then develops the formalism.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The work on an iterative procedure is still going on [16]. First applications to heavy mesons [18] have been carried out, but it is unclear how one can correct for the admitted violation of every possible symmetry. Wegner [33] has proposed an analytic unitary transform which leads to Hamiltonian flow equations.…”

Section: The Light-cone Hamiltonian (Matrix)mentioning

confidence: 99%

On confinement in a light-cone Hamiltonian for QCD

Pauli¹

1999

Eur. Phys. J. C

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Abstract. The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the qq-space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fockspace regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement.

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“…The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.In recent years quantization in the light cone frame has been extensively studied in connection with the discovery of new non-perturbative effects that would be unobservable in the standard spacetime quantization [1][2][3].There are several reasons that make the light cone quantization a method radically different compared to the standard quantization. The dispersion relation…”

mentioning

confidence: 99%

“…In recent years quantization in the light cone frame has been extensively studied in connection with the discovery of new non-perturbative effects that would be unobservable in the standard spacetime quantization [1][2][3].…”

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confidence: 99%

New excitations in the Thirring model

et al. 1998

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The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate x − in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Righthanded fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.In recent years quantization in the light cone frame has been extensively studied in connection with the discovery of new non-perturbative effects that would be unobservable in the standard spacetime quantization [1][2][3].There are several reasons that make the light cone quantization a method radically different compared to the standard quantization. The dispersion relationin the light cone. This implies that the particles and antiparticles occupy disconnected sectors of momentum space. Furthermore, if the momentum k + is discretized by compactifying x − , the energy k − is also quantized and nonzero. Thus, the light cone momentum is never singular if the spacetime topology is S 1 × ℜ [4]. The above comments show that the quantization in the light cone is naturally defined over a manifold with non-trivial topology. As a consequence, one could expect new physical effects originated in the implicit difference in topology from standard spacetime quantization.From this point of view, the massless Thirring model is an example where one could investigate the new effects that emerge in the light-cone frame. We will show below that, contrary to the standard quantization, the non-trivial topology of the light-cone spacetime induces abelian instanton-like excitations, i.e. a purely quantum * E-mail: cortes@leo.unizar.es † E-mail: jgamboa@lauca.usach.cl ‡ E-mail: ischmidt@fis.utfsm.cl § E-mail: jz@cecs.cl mechanical effect that appears in the calculation of the fermionic determinant. Let us consider the massless Thirring model in the light cone framewhere ∂ ± = ∂ ∂x ± and x + and x − play the role of time and space respectively.One should note that (1) is invariant under the charge conjugation symmetry ψ L,R ↔ ψ † L,R , that is expected to be conserved at the quantum level. However in order to quantize the system following the path integral methods it is more convenient to write (1) as followswhereThus, the generating functional,after integrating over the right handed fields is

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Quarkonia in Hamiltonian Light-Front QCD

Cited by 64 publications

References 8 publications

Nonperturbative light-front Hamiltonian methods

Nonperturbative light-front Hamiltonian methods

On confinement in a light-cone Hamiltonian for QCD

New excitations in the Thirring model

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