Aristotle’s &lt;i&gt;Metaphysics&lt;/i&gt; Lambda

Alexandru, Stefan

doi:10.1163/9789004258877

Cited by 7 publications

(5 citation statements)

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“…Discussion in this section thus implicitly assumed that the λ-dependent subtraction of mode density ρ(λ) → ρ sub (λ), needed for proper spectral definition of S, is also used in the definition of S ch . Related details will be discussed elsewhere [12].…”

Section: The Uses: Order Parameters and Finite Volumementioning

confidence: 99%

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Spontaneous chiral symmetry breaking as condensation of dynamical chirality

Alexandru

Horváth

2013

Physics Letters B

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The occurrence of spontaneous chiral symmetry breaking (SChSB) is equivalent to sufficient abundance of Dirac near-zeromodes. However, dynamical mechanism leading to breakdown of chiral symmetry should be naturally reflected in chiral properties of the modes. Here we offer such connection, presenting evidence that SChSB in QCD proceeds via the appearance of modes exhibiting dynamical tendency for local chiral polarization. These modes form a band of finite width Λ ch (chiral polarization scale) around the surface of otherwise anti-polarized Dirac sea, and condense. Λ ch characterizes the dynamics of the breaking phenomenon and can be converted to a quark mass scale, thus offering conceptual means to determine which quarks of nature are governed by broken chiral dynamics. It is proposed that, within the context of SU(3) gauge theories with fundamental Dirac quarks, mode condensation is equivalent to chiral polarization. This makes Λ ch an "order parameter" of SChSB, albeit without local dynamical field representation away from chiral limit. Several uses of these features, both at zero and finite temperature, are discussed. Our initial estimates are Λ ch ≈ 150 MeV (N f = 0), Λ ch ≈ 80 MeV (N f = 2+1, physical point), and that the strange quark is too heavy to be crucially influenced by broken chiral symmetry.

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Section: The Uses: Order Parameters and Finite Volumementioning

confidence: 99%

“…Chiral density ρ ch (λ) is of course not affected by sparse occurrence of low-lying eigenmodes and exhibits a behavior described by Conjecture 2. Detailed account of these calculations, and of the correspondence, will be presented elsewhere [10].…”

Section: Chiral Polarization Scalementioning

confidence: 99%

Spontaneous chiral symmetry breaking as condensation of dynamical chirality

Alexandru

Horváth

2013

Physics Letters B

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“…That occurrence has recently been studied in detail, producing a rather convincing evidence that the anomalous phase is neither an infrared (Ref. [3,13]) nor an ultraviolet (Refs. [12,13]) artifact, and is thus most likely physical.…”

Section: Discussionmentioning

confidence: 97%

“…[3,13]) nor an ultraviolet (Refs. [12,13]) artifact, and is thus most likely physical. This makes it very reasonable to interpret our finding as a manifestation of the fact that many light quarks and thermal bath have very similar disordering effects on chirality, and that we have simply encountered another corner of the theory space where anomalous phase occurs.…”

Section: Discussionmentioning

confidence: 99%

Broken valence chiral symmetry and chiral polarization of Dirac spectrum in Nf=12 QCD at small quark mass

Alexandru

Horváth

2016

AIP Conference Proceedings

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Abstract. The validity of recently proposed equivalence between valence spontaneous chiral symmetry breaking (vSChSB) and chiral polarization of low energy Dirac spectrum (ChP) in SU(3) gauge theory, is examined for the case of twelve massdegenerate fundamental quark flavors. We find that the vSChSB-ChP correspondence holds for regularized systems studied. Moreover, our results suggest that vSChSB occurs in two qualitatively different circumstances: there is a quark mass m c such that for m > m c the mode condensing Dirac spectrum exhibits standard monotonically increasing density, while for m ch < m < m c the peak around zero separates from the bulk of the spectrum, with density showing a pronounced depletion at intermediate scales. Valence chiral symmetry restoration may occur at yet smaller masses m < m ch , but this has not yet been seen by overlap valence probe, leaving the m ch = 0 possibility open. The latter option could place massless N f =12 theory outside of conformal window. Anomalous behavior of overlap Dirac spectrum for m ch < m < m c is qualitatively similar to one observed previously in zero and few-flavor theories as an effect of thermal agitation.

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“…This region is a good candidate for the partially deconfined phase. Recent lattice studies [18,19,20] which reported peculiar properties in this region may be explained as consequences of partial deconfinement.…”

Section: Application To Qcdmentioning

confidence: 96%