calCcalPcalT-invariant two-fermion Dirac equation with extended hyperfine operator

Hund, Viktor; Pilkuhn, H.

doi:10.1088/0953-4075/33/8/311

Cited by 11 publications

(8 citation statements)

References 23 publications

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“…Here we just note as in [19] that in the QGP the quark mass is a "chiral mass", so the derivation of the effective single-body Dirac equation in this case would be a priori different from the one discussed in [25].…”

Section: A Two-body Bound State Problemmentioning

confidence: 99%

“…For an extensive review of the known results on how one can reduce a 2-body relativistic Dirac problem to that of a potential problem we refer to [25]. Here we just note as in [19] that in the QGP the quark mass is a "chiral mass", so the derivation of the effective single-body Dirac equation in this case would be a priori different from the one discussed in [25].…”

Section: A Generalitiesmentioning

confidence: 99%

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Toward a theory of binary bound states in the quark-gluon plasma

2004

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Although at temperatures T ≫ ΛQCD the quark-gluon plasma (QGP) is a gas of weakly interacting quasiparticles (modulo long-range magnetism), it is strongly interacting in the regime T = (1 − 3) Tc. As both heavy ion experiments and lattice simulations are now showing, in this region the QGP displays rather strong interactions between the constituents. In this paper we investigate the relationship between four (previously disconnected) lattice results: i. spectral densities from MEM analysis of correlators; ii. static quark free energies F (R); iii. quasiparticle masses; iv. bulk thermodynamics p(T ). We show a high degree of consistency among them not known before. The potentials V (R) derived from F (R) lead to large number of binary bound states, mostly colored, in gq, qq, gg, on top of the usualqq mesons. Using the Klein-Gordon equation and (ii-iii) we evaluate their binding energies and locate the zero binding endpoints on the phase diagram, which happen to agree with (i). We then estimate the contribution of all states to the bulk thermodynamics in agreement with (iv). We also address a number of theoreticall issues related with to the role of the quark/gluon spin in binding at large αs, although we do not yet include those in our estimates. Also the issue of the transport properties (viscosity, color conductivity) in this novel description of the QGP will be addressed elsewhere.

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Section: A Two-body Bound State Problemmentioning

confidence: 99%

Section: A Generalitiesmentioning

confidence: 99%

Toward a theory of binary bound states in the quark-gluon plasma

2004

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“…It has not been possible to calculate these masses analytically since the interactions just above T c are supposed to be strong and hence nonperturbative. Weldon [12] obtained in perturbation theory a somewhat complicated formula involving momentum for the dispersion relation which could however be approximated to within ∼ 10 % by p 2 0 ≈ m 2 q + p 2 with m q a temperature dependent quantity which could be used as an effective mass in a simple hydrogenic model derived from Bethe-Salpeter equation as done in [13] following the argument of Hund and Pilkhun [14]. Remarkably, despite the presence of the effective mass, the helicity remains conserved as the quark wave function satisfies a free Dirac equation.…”

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confidence: 99%

Matter Formed at the BNL Relativistic Heavy Ion Collider

Brown

Gelman²,

Rho³

2006

Phys. Rev. Lett.

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We suggest that the "new form of matter" found just above Tc by RHIC is made up of tightly bound quark-antiquark pairs, essentially 32 chirally restored (more precisely, nearly massless) mesons of the quantum numbers of π, σ, ρ and a1. Taking the results of lattice gauge simulations (LGS) for the color Coulomb potential from the work of the Bielefeld group and feeding this into a relativistic two-body code, after modifying the heavy-quark lattice results so as to include the velocity-velocity interaction, all ground-state eigenvalues of the 32 mesons go to zero at Tc just as they do from below Tc as predicted by the vector manifestation (VM in short) of hidden local symmetry. This could explain the rapid rise in entropy up to Tc found in LGS calculations. We argue that how the dynamics work can be understood from the behavior of the hard and soft glue.

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“…The replacement of 1 / m N by m N / m 12 2 in the static Dirac equation is due to Breit (at the order ͑Z␣͒ 6 , m 12 −2 is replaced by E −2 [4,5], which requires new orthogonality relations in the variable r E = Er [2]). The standard hyperfine operator contains only the Hermitian part ͓V , ١͔ /2 of V١; the anti-Hermitian part ͕V , ١͖ / 2 contributes to hyperfine mixing (in the 16-component formalism, the mixing arises from the retardation part of the Breit operator).…”

Section: ͑8͒mentioning

confidence: 99%

Relativistic recoil in radiative atomic transitions

Pilkuhn

2004

Phys. Rev. A

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A modified time-dependent perturbation theory for single-photon emission is proposed, which yields the exact photon energy for a relativistically recoiling atom. The relevant unperturbed "Hamiltonian" has stationary eigenvalues E 2 . Its form is generalized here to hydrogenic atoms of arbitrary nuclear spins.When an atom of mass M emits or absorbs a single photon of momentum បk, it suffers a recoil, which is used for example in laser cooling. In emission from an atom at rest, the nonrelativistic recoil energy is P 2 /2M. From momentum conservation P + បk = 0 and with k = / c, the corresponding photon energy ប is ⌬E − ͑⌬E͒ 2 /2Mc 2 , where ⌬E = E − EЈ is the difference of the initial and final atomic energy levels. More precisely, EЈ is the total energy of the final atomic state in its own rest frame, which for the ground state is just Mc 2 (c 2 times the sum of the masses of its constituents, minus the total binding energy). Another nonrelativistic expression for ប is thus ⌬E − ͑⌬E͒ 2 /2EЈ. However, relativistic energy conservation requires E = ប + ͑EЈ 2 + ប 2 2 ͒ 1/2 , which leads to

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calCcalPcalT-invariant two-fermion Dirac equation with extended hyperfine operator

Cited by 11 publications

References 23 publications

Toward a theory of binary bound states in the quark-gluon plasma

Toward a theory of binary bound states in the quark-gluon plasma

Matter Formed at the BNL Relativistic Heavy Ion Collider

Relativistic recoil in radiative atomic transitions

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