Gauged Dirac operator on the quantum sphere in instanton sector

2020 ◽  
Vol 35 (08) ◽  
pp. 2050048
Author(s):  
M. Lotfizadeh
Keyword(s):  
Dirac Operator ◽  
Fuzzy Sphere ◽  
Limit Case ◽  
Quantum Sphere ◽  
Noncommutative Parameter

In this paper, we construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. Using the [Formula: see text]-deformed fuzzy Ginsparg–Wilson algebra, we study the [Formula: see text]-deformed gauged fuzzy Dirac and chirality operators in instanton sector. We will show the correct fuzzy sphere limit in the limit case [Formula: see text] and the correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.

q-deformed fuzzy Ginsparg–Wilson algebra and its q-deformed Dirac and chirality operators on quantum fuzzy two-sphere

2020 ◽  
Vol 17 (10) ◽  
pp. 2050154
Author(s):  
M. Lotfizadeh ◽  
Ebrahim Nouri Asl
Keyword(s):  
Fuzzy Sphere ◽  
Limit Case ◽  
Noncommutative Parameter

We construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. We will show that there are a class of these operators on [Formula: see text] in which all of them in the limit case [Formula: see text] has the correct fuzzy sphere limit as well as they have correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.

Super Ginsparg–Wilson algebra and Dirac operator on the super fuzzy Euclidean hyperboloid EAdSF(2|2)

2020 ◽  
Vol 35 (31) ◽  
pp. 2050196
Author(s):  
M. Lotfizadeh
Keyword(s):  
Dirac Operator ◽  
Gauge Fields ◽  
Hopf Fibration ◽  
Limit Case ◽  
Noncommutative Parameter

In this paper, we construct super fuzzy Dirac and chirality operators on the super fuzzy Euclidean hyperboloid [Formula: see text] in-instanton and no-instanton sectors. Using the super pseudo-projectors of the noncompact first Hopf fibration, we construct the Ginsparg–Wilson algebra in instanton and no-instanton sectors. Then, using the generators of this algebra, we construct pseudo super-Dirac and chirality operators in both sectors. We also construct pseudo super-Dirac and chirality operators corresponding to the case in which our theory includes gauge fields. We show that they have correct commutative limit in the limit case when the noncommutative parameter [Formula: see text] tends to infinity.

Fuzzy conifold YF6 and Dirac operator of principal fibration XF5 → SF2 × SF2

2020 ◽  
Vol 35 (18) ◽  
pp. 2050088
Author(s):  
M. Lotfizadeh
Keyword(s):  
Dirac Operator ◽  
Limit Case ◽  
Base Manifold ◽  
Noncommutative Parameter

It has been constructed the fuzzy Dirac and chirality operators on fuzzy [Formula: see text] which is the base manifold of the principal fibration [Formula: see text]. Using the fuzzy Ginsparg–Wilson algebra, it has been studied the gauged fuzzy Dirac and chirality operators in instanton sector. It has been shown that they have correct commutative limit in the limit case when noncommutative parameter [Formula: see text] tends to infinity.

scholarly journals DIFFERENTIAL CALCULUS ON FUZZY SPHERE AND SCALAR FIELD

1998 ◽  
Vol 13 (19) ◽  
pp. 3235-3243 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Scalar Field ◽  
Dirac Operator ◽  
Differential Calculus ◽  
Spectral Triple ◽  
Fuzzy Sphere ◽  
Alternative Possibility ◽  
Operator Ordering

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.

scholarly journals The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

2008 ◽  
Vol 279 (1) ◽  
pp. 77-116 ◽  
Author(s):  
Francesco D’Andrea ◽  
Ludwik Da̧browski ◽  
Giovanni Landi
Keyword(s):  
Dirac Operator ◽  
Quantum Sphere

scholarly journals Dirac operator on the standard Podleś quantum sphere

2003 ◽  
Author(s):  
Ludwik Dąbrowski ◽  
Andrzej Sitarz
Keyword(s):  
Dirac Operator ◽  
Quantum Sphere

scholarly journals NONCOMMUTATIVE QUANTUM MECHANICS: THE TWO-DIMENSIONAL CENTRAL FIELD

2002 ◽  
Vol 17 (19) ◽  
pp. 2555-2565 ◽  
Author(s):  
J. GAMBOA ◽  
F. MÉNDEZ ◽  
M. LOEWE ◽  
J. C. ROJAS
Keyword(s):  
Quantum Mechanics ◽  
Central Field ◽  
Two Dimensional ◽  
Limit Case ◽  
Polynomial Type ◽  
Noncommutative Quantum Mechanics ◽  
The Green Function ◽  
Noncommutative Plane ◽  
Noncommutative Quantum ◽  
Noncommutative Parameter

Quantum mechanics in a noncommutative plane is considered. For a general two-dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter (θ) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of θ and for nonpolynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.

scholarly journals "SCHWINGER MODEL" ON THE FUZZY SPHERE

2010 ◽  
Vol 25 (37) ◽  
pp. 3151-3167 ◽  
Author(s):  
E. HARIKUMAR
Keyword(s):  
Partition Function ◽  
Field Strength ◽  
Dirac Operator ◽  
Path Integral ◽  
Integral Method ◽  
Gauge Fields ◽  
Fuzzy Sphere ◽  
Schwinger Model ◽  
Spinor Fields ◽  
Path Integral Method

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

scholarly journals The dirac operator on the fuzzy sphere

1995 ◽  
Vol 33 (2) ◽  
pp. 171-181 ◽  
Author(s):  
H. Grosse ◽  
P. Prešnajder
Keyword(s):  
Dirac Operator ◽  
Fuzzy Sphere

scholarly journals Dirac operator on the q-deformed fuzzy sphere and its spectrum

2006 ◽  
Vol 2006 (09) ◽  
pp. 037-037 ◽  
Author(s):  
E Harikumar ◽  
Amilcar R Queiroz ◽  
Paulo Teotonio-Sobrinho
Keyword(s):  
Dirac Operator ◽  
Fuzzy Sphere
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