scholarly journals The spectrum of the Dirac operator on coset spaces with homogeneous gauge fields

2003 ◽  
Vol 2003 (05) ◽  
pp. 018-018 ◽  
Author(s):  
Brian P Dolan
Keyword(s):  
Dirac Operator ◽  
Gauge Fields ◽  
Coset Spaces

SPECTRAL FLOW OF HERMITIAN WILSON–DIRAC OPERATOR AND THE INDEX THEOREM IN ABELIAN GAUGE THEORIES ON FINITE LATTICES

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1943-1950 ◽  
Author(s):  
T. FUJIWARA
Keyword(s):  
Dirac Operator ◽  
Gauge Theories ◽  
Index Theorem ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Continuous Family ◽  
Spectral Flow ◽  
Abelian Gauge ◽  
Characteristic Structure ◽  
Finite Lattices

The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field configurations. It is also argued that in two dimensions the eigenvalue spectra for some special but nontrivial background gauge fields can be described by a set of universal polynomials and the index can be found exactly.

scholarly journals Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
A. Bochniak ◽  
A. Sitarz ◽  
P. Zalecki
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Gauge Fields ◽  
Wick Rotation ◽  
Spectral Action ◽  
Geometry Model ◽  
The Standard Model ◽  
Cp Symmetry

Abstract We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological θ-terms for the electroweak gauge fields.

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 Gauge fields on coset spaces

1978 ◽  
Vol 44 (2) ◽  
pp. 318-330 ◽  
Author(s):  
G. Domokos ◽  
S. Kövesi-Domokos
Keyword(s):  
Gauge Fields ◽  
Coset Spaces

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.

Zero Modes of the Dirac Operator in Vortex-Type Gauge Fields

2004 ◽  
Vol 140 (3) ◽  
pp. 1241-1252
Author(s):  
V. Ch. Zhukovsky ◽  
O. V. Tarasov
Keyword(s):  
Dirac Operator ◽  
Gauge Fields ◽  
Zero Modes

Pseudo generalization of Ginsparg–Wilson algebra on the fuzzy EAdS2 including gauge fields

2020 ◽  
Vol 17 (03) ◽  
pp. 2050046 ◽  
Author(s):  
M. Lotfizadeh ◽  
Ebrahim Nouri Asl
Keyword(s):  
Dirac Operator ◽  
Gauge Fields

Using the gauged pseudo-Hermitian fuzzy Ginsparg–Wilson algebra, pseudo fuzzy Dirac and chirality operators on the fuzzy [Formula: see text] have been studied. Also, the spectrum of the gauged pseudo fuzzy Dirac operator in the instanton sector has been studied.

scholarly journals DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS

2012 ◽  
Vol 27 (25) ◽  
pp. 1230024 ◽  
Author(s):  
E. A. IVANOV ◽  
A. V. SMILGA
Keyword(s):  
Quantum Mechanics ◽  
Dirac Operator ◽  
Complex Manifold ◽  
Simple Formula ◽  
Supersymmetric Quantum Mechanics ◽  
Gauge Fields ◽  
Complex Manifolds ◽  
Sum Formula ◽  
External Gauge ◽  
Dolbeault Complex

We explore a simple [Formula: see text] supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum [Formula: see text] can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah–Singer theorem.

GAUGE FIELDS ON THE FUZZY SPHERE

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2431-2438 ◽  
Author(s):  
Peter Prešnajder
Keyword(s):  
Gauge Symmetry ◽  
Dirac Operator ◽  
Spinor Field ◽  
Gauge Fields ◽  
Fuzzy Sphere ◽  
Commutative Case

The free spinor field on a fuzzy sphere is described within Watamura approach to Dirac operator. Except of the highest mode, its spectrum is the same but truncated as in the commutative case. We present a simple gauge extension of the model with usual polynomial interaction. The gauge symmetry is exact, and the chiral properties of the field modes are standard except the highest mode.

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