Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications
International Journal of Mathematics and Mathematical Sciences, 2007 Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers.
M. Aslam Chaudhry, Asghar Qadir
doaj +1 more source
The Wilson Dirac Spectrum for QCD with Dynamical Quarks
, 2011 All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case with two light ...
Splittorff, K., Verbaarschot, J. J. M.
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On the Dolbeault–Dirac operator of quantized symmetric spaces [PDF]
, 2013 The Dolbeault complex of a quantized compact Hermitian symmetric space is expressed in terms of the Koszul complex of a braided symmetric algebra of Berenstein and Zwicknagl.
U. Kraehmer, Matthew Tucker-Simmons
semanticscholar +1 more source
Supercharge Operator of Hidden Symmetry in the Dirac Equation
, 2006 As is known, the so-called Dirac $K$-operator commutes with the Dirac Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is degenerate with respect to two signs of its eigenvalues. This degeneracy may be described by some operator,
Khachidze, Tamari~T. +1 more
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Topologically invariant transformation for lattice fermions [PDF]
, 2000 A transformation is devised to convert any lattice Dirac fermion operator into a Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O(a) lattice artifacts, has ...
Chiu, Ting-Wai
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Incomplete inverse spectral and nodal problems for Dirac operator
Advances in Differential Equations, 2015 The incomplete inverse spectral and inverse nodal problems for Dirac operator defined on a finite interval with separated boundary conditions are considered. We prove uniqueness theorems for the so-called incomplete inverse spectral problem.
Zhaoying Wei +2 more
semanticscholar +1 more source
On Quantitative Bounds on Eigenvalues of a Complex Perturbation of a Dirac Operator [PDF]
, 2013 We prove a Lieb–Thirring type inequality for a complex perturbation of a d-dimensional massive Dirac operator $${D_m, m\geq 0, d \geq 1}$$Dm,m≥0,d≥1 whose spectrum is $${]-\infty,-m]\cup[m,+\infty[}$$]-∞,-m]∪[m,+∞[ .
C. Dubuisson
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Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
, 1998 We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model.
Farchioni, F., Hip, I., Lang, C. B.
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Spectral properties of the Wilson-Dirac operator and random matrix theory [PDF]
, 2013 Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson Dirac operator.
M. Kieburg +2 more
semanticscholar +1 more source
Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson-Dirac Operator [PDF]
SIAM Journal on Scientific Computing, 2013 In lattice quantum chromodynamics (QCD) computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers show critical slowing down for large system sizes and physically interesting ...
A. Frommer +4 more
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