scholarly journals Dirac operator spectral density and low energy sum rules

2000 ◽  
Vol 2000 (06) ◽  
pp. 025-025 ◽  
Author(s):  
K Zyablyuk
Keyword(s):  
Dirac Operator ◽  
Spectral Density ◽  
Sum Rules ◽  
Low Energy

scholarly journals EFFECTIVE LOW-ENERGY THEORIES AND QCD DIRAC SPECTRA

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1404-1415 ◽  
Author(s):  
D. TOUBLAN ◽  
J. J. M. VERBAARSCHOT
Keyword(s):  
Partition Function ◽  
Dirac Operator ◽  
Spectral Density ◽  
Random Matrix ◽  
Matrix Theory ◽  
Low Energy ◽  
Effective Theory ◽  
Kinetic Term ◽  
Dirac Spectrum ◽  
Energy Theory

We analyze the smallest Dirac eigenvalues by formulating an effective theory for the Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra (with eigenvalues scattered in the complex plane) in terms of an effective low energy theory.

ROLE OF THE ELECTRON–PHONON INTERACTION ON THE SPECTRAL DENSITY AND PSEUDOGAP IN CUPRATES

2002 ◽  
Vol 16 (23) ◽  
pp. 3465-3471
Author(s):  
I. CHAUDHURI ◽  
S. K. GHATAK
Keyword(s):  
Critical Temperature ◽  
Spectral Density ◽  
Low Energy ◽  
Phonon Interaction ◽  
Energy Excitation ◽  
Electron Phonon Interaction ◽  
Peak Structure ◽  
Electronic Model ◽  
Jahn Teller

The pseudogap structure in low energy excitation in cuprates appears below a temperature and the spectral density exhibits strong wave-vector dependence. An electronic model that emphasized the coupling of carrier in Cu-O with phonon is examined for pseudogap. The electron–phonon interaction originates from the modulation of on-site and hopping energy and leads to spontaneous Jahn–Teller-like distortion and pseudogap below a critical temperature. At low temperature the spectral density has two-peak structure about the Fermi level for all k along Γ-M whereas such structure exists along Γ-X for small k only. The magnitude of pseudogap shows strong k-dependence — maximum along Γ-M and vanishes along Γ-X. These features emphasize the role of electron–phonon interaction in formation of pseudogap.

Derivative sum rules and inconsistencies in the low-energy N scattering parameters

1969 ◽  
Vol 11 (1) ◽  
pp. 115-126 ◽  
Author(s):  
N.M. Queen ◽  
S. Leeman ◽  
F.E. Yeomans
Keyword(s):  
Sum Rules ◽  
Low Energy ◽  
Scattering Parameters

scholarly journals Low energy sum rules forπ−πscattering and threshold parameters

1996 ◽  
Vol 53 (5) ◽  
pp. 2362-2370 ◽  
Author(s):  
B. Ananthanarayan ◽  
D. Toublan ◽  
G. Wanders
Keyword(s):  
Sum Rules ◽  
Low Energy

scholarly journals Analysis of the DD¯⁎K System with QCD Sum Rules

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Zun-Yan Di ◽  
Zhi-Gang Wang
Keyword(s):  
Spectral Density ◽  
Sum Rules ◽  
Resonance State ◽  
Energy Scale ◽  
Color Singlet ◽  
Qcd Sum Rules ◽  
Optimal Energy ◽  
Numerical Result ◽  
The Future ◽  
Vacuum Condensates

In this article, we construct the color singlet-singlet-singlet interpolating current with IJP=3/21- to study the DD¯⁎K system through QCD sum rules approach. In calculations, we consider the contributions of the vacuum condensates up to dimension-16 and employ the formula μ=MX/Y/Z2-2Mc2 to choose the optimal energy scale of the QCD spectral density. The numerical result MZ=4.71-0.11+0.19 GeV indicates that there exists a resonance state Z lying above the DD¯⁎K threshold to saturate the QCD sum rules. This resonance state Z may be found by focusing on the channel J/ψπK of the decay B→J/ψππK in the future.

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

scholarly journals Statistical properties of the spectrum of the QCD Dirac operator at low energy

2001 ◽  
Vol 603 (1-2) ◽  
pp. 343-368 ◽  
Author(s):  
D. Toublan ◽  
J.J.M. Verbaarschot
Keyword(s):  
Dirac Operator ◽  
Statistical Properties ◽  
Low Energy
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