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.

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.

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.

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

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.

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 DIRAC OPERATORS ON LIE ALGEBROIDS

2021 ◽  
pp. 983
Author(s):  
Arezo Tarviji ◽  
Morteza Mirmohammad Rezaei
Keyword(s):  
Dirac Operator ◽  
Spin Structure ◽  
Dirac Operators ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Eigenvalue Bounds ◽  
Base Manifold ◽  
Spinor Bundle ◽  
Complex Spin ◽  
The One

We compare the Dirac operator on transitive Riemannian Lie algebroid equipped by spin or complex spin structure with the one defined on to its base manifold‎. Consequently we derive upper eigenvalue bounds of Dirac operator on base manifold of spin Lie algebroid twisted with the spinor bundle of kernel bundle‎.

Loving the Other Beyond Death

2018 ◽  
Vol 40 (2) ◽  
pp. 147-155
Author(s):  
Kas Saghafi
Keyword(s):  
The Other ◽  
Limit Case ◽  
Western Tradition

Turning to an example provided by Aristotle and taken up by Derrida in Politics of Friendship, which functions as a limit case—loving the other beyond death—I argue that Derrida's short-lived term, aimance, gently and lovingly contests the primacy given either to love or to friendship in the Western tradition, but also to the living act of loving and the figure of the lover, putting pressure on the very conceptual differences between these terms.

scholarly journals Extended supersymmetries and the Dirac operator

2005 ◽  
Vol 315 (2) ◽  
pp. 467-487 ◽  
Author(s):  
A. Kirchberg ◽  
J.D. Länge ◽  
A. Wipf
Keyword(s):  
Dirac Operator

World Literature, the opaque archive, and the untranslatable: J. M. Coetzee and some others

2021 ◽  
pp. 002198942098874
Author(s):  
Andrew van der Vlies
Keyword(s):  
South African ◽  
Nobel Prize ◽  
Cultural Production ◽  
World Literature ◽  
Virtual Space ◽  
Limit Case ◽  
Global Community ◽  
Theoretical Orientations ◽  
Disciplinary Field

A key concern of recent theoretical orientations in the development of “World Literature” as a discipline has been the question of accessibility to literatures in minor languages, which is to say of literal and metaphorical translatability, even transparency. This essay explores the challenge posed by the occlusion of the possible intertextual influence of works in such languages that are evident only as a trace in texts that now seem indisputably part of a canon of World Literature. What happens when the engagement of writers in this canon with cultural production in languages adjacent to those in which they themselves principally operate is not evident to an increasingly global community of scholars, and perhaps not even evidenced in an author’s archive (whether this is understood to be a material collection or indeed a virtual space conceptualized as the literary ecosystem in which an author has developed)? This essay addresses these questions with reference to the work of South African-born Nobel Prize-winning writer J. M. Coetzee, and to the problem posed by some of his work’s (and his archive’s) others, here specifically Afrikaners and the work of Afrikaans-language writers. This consideration has implications not only for the current shape of Coetzee studies, but for that of World Literature more broadly, presenting something of a limit-case for the translation metaphor that directs some of its formulations as disciplinary field.

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