Boosting equal time bound states

Dietrich, Dennis D.; Hoyer, Paul; Järvinen, Matti

doi:10.1103/physrevd.85.105016

Cited by 21 publications

(21 citation statements)

References 13 publications

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“…Because the field theory is Poincaré invariant and is solved at lowest order in the coupling e, with the Poincaré invariant boundary condition (1.5), we expect the state (1.7) to be covariant. In [24] we verified this in D = 1 + 1 dimensions using the boost generator M 01 . The boosted state satisfies the bound-state equation (1.10) with the appropriately shifted momentum, i.e.,…”

Section: Arxiv:12124747v2 [Hep-ph] 19 Mar 2013mentioning

confidence: 53%

“…The present paper is a sequel to our study [24] of Poincaré invariance. Here we examine other features of the solutions to the bound-state equation (1.10) in D = 1 + 1.…”

Section: Arxiv:12124747v2 [Hep-ph] 19 Mar 2013mentioning

confidence: 99%

“…We take the coefficient of We showed in [24] that E = √ P 2 + M 2 and worked out the P dependence of the wave function. It turned out to be convenient to introduce the variable…”

Section: Solutions Of the Two-fermion Bound-state Equation Inmentioning

confidence: 99%

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Towards a Born term for hadrons

2013

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We study bound states of Abelian gauge theory in D = 1 + 1 dimensions using an equal-time, Poincaré-covariant framework. The normalization of the linear confining potential is determined by a boundary condition in the solution of Gauss' law for the instantaneous A 0 field. As in the case of the Dirac equation, the norm of the relativistic fermion-antifermion (ff ) wave functions gives inclusive particle densities. However, while the Dirac spectrum is known to be continuous we find that regular ff solutions exist only for discrete bound-state masses. The ff wave functions are consistent with the parton picture when the kinetic energy of the fermions is large compared to the binding potential. We verify that the electromagnetic form factors of the bound states are gauge invariant and calculate the parton distributions from the transition form factors in the Bjorken limit. For relativistic states we find a large sea contribution at low xBj. Since the potential is independent of the gauge coupling the bound states may serve as "Born terms" in a perturbative expansion, in analogy to the usual plane wave in and out states.

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Section: Arxiv:12124747v2 [Hep-ph] 19 Mar 2013mentioning

confidence: 53%

“…The present paper is a sequel to our study [24] of Poincaré invariance. Here we examine other features of the solutions to the bound-state equation (1.10) in D = 1 + 1.…”

Section: Arxiv:12124747v2 [Hep-ph] 19 Mar 2013mentioning

confidence: 99%

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Towards a Born term for hadrons

2013

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“…The whole contribution to the BS amplitude comes here from the instan-ton sectors N = ±1. The r -dependence of the ratio of contraction-although in another layout-has been observed in [16,17].…”

Section: Boosted Framementioning

confidence: 88%

“…Several works have been devoted to the investigation of this effect for the bound-state wave function in the case of hydrogen atom, positronium, nuclei or model systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. When the relativistic motion of a primarily nonrelativistic system as for instance a hydrogen atom is considered, QFT phenomena appear, and the problem is no longer purely quantum mechanical but requires a field theoretical approach.…”

Section: Introductionmentioning

confidence: 99%

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

Radożycki

2015

Eur. Phys. J. C

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The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the twodimensional massless quantum electrodynamics (the socalled Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties.

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Applications to QCD Bound States

Hoyer

2021

SpringerBriefs in Physics

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I consider the frame dependence of QCD bound states in the presence of a confining, spatially constant gluon field energy density. The states are quantized at equal time in A 0 = 0 (temporal) gauge. I derive the frame dependence of the wave functions, and demonstrate the Lorentz covariance of the electromagnetic (transition) form factors for states of any spin. The wave functions of J P C = 0 −+ states with CM momentum P = 0 are considered in some detail, verifying their local normalizability and the expected frame dependence of the bound state energy. I. REMARKS ON BOUND STATESAtoms and hadrons are our primary examples of physical bound states. Their field theory (QED and QCD) description complements the methods of scattering amplitudes, but is not part of the standard QFT curriculum. Bound states are challenging, but the omission even of their general principles seems unwarranted.Analytic evaluations of Standard Model dynamics mainly rely on expansions in powers of the coupling. The lowest order term should provide an adequate first approximation of the full result. Scattering amplitudes reduce to free propagators at vanishing coupling, which defines the lowest order of the perturbative S-matrix.Bound state constituents interact at all times. Bound states are typically expanded around solutions of the Schrödinger or Bethe-Salpeter type equations. The choice of initial (non-perturbative) state affects its higher order perturbative corrections such that the full series (for physical quantities) is formally independent of the initial choice [1,2].Each order of a perturbative expansion must have Poincaré symmetry. The explicit covariance of Feynman diagrams is enabled by their free propagators. Bound states are eigenstates of the Hamiltonian, which is frame dependent. Consequently bound state covariance is not fully explicit (kinetic), but also realized dynamically (through interactions). E.g., time translation invariance is ensured for eigenstates of the Hamiltonian, which includes interactions.In equal-time quantization the Hamiltonian commutes with space translations and rotations, but not with boosts. Bound state masses and quantum numbers can be determined in the rest frame [3][4][5][6], whereas bound state scattering involves moving states. The frame dependence of atoms is dynamic and non-trivial [7][8][9].Hamiltonians quantized at equal light-front (LF) time x + ≡ t + z commute with boosts [10,11]. Photons propagating in the negative z-direction interact at equal x + , making LF wave functions advantageous for describing form factors. Rotation symmetry is realized dynamically on the LF since x + depends on z. This complicates the determination of angular momentum (except J z ), and raises some delicate issues [12,13].

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Boosting equal time bound states

Cited by 21 publications

References 13 publications

Towards a Born term for hadrons

Towards a Born term for hadrons

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

Applications to QCD Bound States

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