On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3)

Macfarlane, Alan; Sudbery, Anthony; Weisz, Peter

doi:10.1007/bf01654302

Cited by 174 publications

(186 citation statements)

References 9 publications

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“…The sum of the last two terms in the second line of (74) can be rewritten using the following relation between the structure constants of the SU(N) group [27] …”

Section: The Su (N ) × Su (N ) Meson Model In 2pi-hartree Approximationmentioning

confidence: 99%

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

2008

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Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the one-and two-point functions. The non-perturbative counterterms are deduced from the conditions for the cancellation of the overall and the subdivergences in the complete Hartree-Dyson-Schwinger equations, with a transparent method. The procedure proposed in the present paper is shown to be equivalent to the iterative renormalisation method of Blaizot et al.[1]. MotivationOne of the most popular approximation techniques in many-body quantum theory is the Hartree approximation. In quantum field theory it corresponds to the momentum independent two-loop truncation of the two-particle irreducible effective action. It is used extensively both in equilibrium [2,3,4] and out-of-equilibrium [5,6,7,8] non-perturbative investigations of phase transition phenomena. Its non-perturbative renormalisability was demonstrated as particular case of the general proof of renormalisability of the physical quantities computed in various 2PI approximations [9,1,10]. These proofs are rather involved especially in the broken symmetry phase. For this reason in many practical applications the renormalised equations are not constructed explicitly. For instance, investigations of the finite temperature phase transitions in strongly interacting matter frequently either omit zero temperature quantum corrections in the 2PI approximate equations of the relevant 1-and 2-point functions [3,4,11] or take into account vacuum fluctuations by applying some cut-off [12].The exact generating 2PI-functional Γ[Φ, G] fulfils generalised Ward-Takahashi identities reflecting global internal symmetries of the models. As a consequence the 1PI effective potential Γ[Φ, G(Φ)]

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“…The sum of the last two terms in the second line of (74) can be rewritten using the following relation between the structure constants of the SU(N) group [27] …”

Section: The Su (N ) × Su (N ) Meson Model In 2pi-hartree Approximationmentioning

confidence: 99%

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

2008

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“…From this we obtained the rational R-matrix with adjoint SU(n) symmetry, given in (20), as well as the corresponding integrable Hamiltonian. From the physics point of view the main problem with the latter is its lack of hermiticity, which renders its physical interpretation unclear.…”

Section: Resultsmentioning

confidence: 99%

“…, where w a is the unique vector such that e 1n = a w a I a , the norms can be computed easily using [20] a Table 1. Highest-weight vectors for the irreducible submodules in the decomposition of (5).…”

Section: Adjoint Representation Of Su(n)mentioning

confidence: 99%

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On rationalR-matrices with adjoint SU(n) symmetry

Stronks¹,

Leur²,

Schuricht³

2016

J. Phys. A: Math. Theor.

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“…[30]. Since we are only concerned with oscillation physics, our Hamiltonian can be made traceless, and it is, of course, Hermitian.…”

Section: Ementioning

confidence: 99%

Parametric enhancement of flavor oscillation in a three-neutrino framework

Merfeld

Latimer

2014

Phys. Rev. C

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When neutrinos travel through matter with a periodic density profile, the neutrino oscillation probability can be enhanced if certain conditions are satisfied. In a two-neutrino framework, the condition for parametric resonance is known. Herein, we consider the analogous parametric resonance condition within the context of a full three-neutrino framework with two oscillation scales. For energies in the range of hundreds of MeV to a few GeV, we find that neutrino oscillation can be parametrically enhanced if two approximate relations are satisfied. The first is similar to the two-neutrino parametric resonance condition while the second involves the other oscillation scale. Treating the Earth's density as piecewise constant, we show that oscillations in this energy range can be enhanced between two-and threefold.

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On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3)

Cited by 174 publications

References 9 publications

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

On rationalR-matrices with adjoint SU(n) symmetry

Parametric enhancement of flavor oscillation in a three-neutrino framework

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