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.

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 A confining quark model and new gauge symmetry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450120 ◽  
Author(s):  
Jong-Ping Hsu
Keyword(s):  
Gauge Symmetry ◽  
Quark Model ◽  
Power Counting ◽  
Gauge Fields ◽  
Linear Potential ◽  
Field Equations ◽  
Color Charge ◽  
Gauge Bosons ◽  
Gauge Transformations ◽  
Empirical Potentials

We discuss a confining model for quark–antiquark system with a new color SU3 gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge gs and find [Formula: see text]. The rules for Feynman diagrams involve propagators with poles of order 2 associated with new gauge fields. The confining quark model may be renormalizable by power counting and compatible with perturbation theory.

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 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 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 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 A Gauge Theory that Mixes Bosonic and Fermionic Gauge Fields

2020 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Gauge Transformation ◽  
Cosmological Term ◽  
Gauge Fields ◽  
Fermionic Field ◽  
Yang Mills

Using a gauge symmetry derived by applying the Dirac constraint formalism to supergravity with a cosmological term in 2 + 1 dimensions, we construct a gauge theory with many characteristics of Yang-Mills theory. The gauge transformation mixes two Bosonic fields and one Fermionic field.

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