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Collapsing and diractype operators
 Geom. Dedicata
"... Abstract. We analyze the limit of the spectrum of a geometric Diractype operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the spectrum of a certain firstorder differential opera ..."
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Cited by 6 (0 self)
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Abstract. We analyze the limit of the spectrum of a geometric Diractype operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the spectrum of a certain firstorder differential
Gauge Theories of Dirac Type
, 2005
"... A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of YangMills gauge theories without making use of a Higgs potential. In more physical terms, it is show ..."
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A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of YangMills gauge theories without making use of a Higgs potential. In more physical terms, it is shown that the Yukawa coupling of fermions, together with gravity, necessarily yields a symmetry reduction provided the fermionic mass is considered as a globally welldefined concept. The structure of this symmetry breaking is shown to be compatible with the symmetry breaking that is induced by the Higgs potential of the minimal Standard Model. As a consequence, it is shown that the fermionic mass has a simple geometrical interpretation in terms of curvature and that the (semiclassical) “fermionic vacuum ” determines the intrinsic geometry of spacetime. We also discuss the issue of “fermion doubling ” in some detail and introduce a specific projection onto the “physical subspace ” that is motivated from the Standard Model.
Gauge Theories of Dirac Type
, 2005
"... A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of YangMills gauge theories without making use of a Higgs potential. In more physical terms, it is show ..."
Abstract

Cited by 5 (2 self)
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A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of YangMills gauge theories without making use of a Higgs potential. In more physical terms, it is shown that the Yukawa coupling of fermions, together with gravity, necessarily yields a symmetry reduction provided the fermionic mass is considered as a globally welldefined concept. The structure of this symmetry breaking is shown to be compatible with the symmetry breaking that is induced by the Higgs potential of the minimal Standard Model. As a consequence, it is shown that the fermionic mass has a simple geometrical interpretation in terms of curvature and that the (semiclassical) “fermionic vacuum ” determines the intrinsic geometry of spacetime. We also discuss the issue of “fermion doubling ” in some detail and introduce a specific projection onto the “physical subspace ” that is motivated from the Standard Model.
A Note on the Square of Dirac Type Differential Operators
, 2006
"... The aim of this note is to present a new global formula for the Lichnerowicz decomposition of a general Dirac type first order differential operator. This formula generalizes the wellknown Lichnerowicz formula for Dirac type operators which are determined by Clifford connections on an arbitrary Cl ..."
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The aim of this note is to present a new global formula for the Lichnerowicz decomposition of a general Dirac type first order differential operator. This formula generalizes the wellknown Lichnerowicz formula for Dirac type operators which are determined by Clifford connections on an arbitrary
FUNDAMENTAL SOLUTIONS FOR DIRACTYPE OPERATORS
"... Abstract. We consider the Diractype operators D + a, a is a paravector in the Clifford algebra. For this operator we state a CauchyGreen formula in the spaces C 1 (G) and W 1 p (G). Further, we consider the Cauchy problem for this operator. 1. Preliminaries. Dirac and Diractype operators are con ..."
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Abstract. We consider the Diractype operators D + a, a is a paravector in the Clifford algebra. For this operator we state a CauchyGreen formula in the spaces C 1 (G) and W 1 p (G). Further, we consider the Cauchy problem for this operator. 1. Preliminaries. Dirac and Diractype operators
Residues Of The Eta Function For An Operator Of Dirac Type
 J. FUNCT ANAL
, 1992
"... We compute the asymptotics of Tr L 2 (P e \GammatP 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the eta function. ..."
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Cited by 30 (6 self)
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We compute the asymptotics of Tr L 2 (P e \GammatP 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the eta function.
The Dirac equation vs. the Dirac type tensor equation
, 2008
"... We discuss a connection between the Dirac equation for an electron and the Dirac type tensor equation with U(1) gauge symmetry. In the previous paper [2], using results of P. Dirac [4], D. Ivanenko and L. Landau [5], E. Kähler [6], F. Gürsey [7], D. Hestenes [8], [9], we present the, socalled, Dira ..."
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We discuss a connection between the Dirac equation for an electron and the Dirac type tensor equation with U(1) gauge symmetry. In the previous paper [2], using results of P. Dirac [4], D. Ivanenko and L. Landau [5], E. Kähler [6], F. Gürsey [7], D. Hestenes [8], [9], we present the, so
Diractype operators on manifolds with boundary
, 2004
"... The hinvariant, Maslov index, and spectral flow for ..."
Boundary value problems for Diractype equations, with apllications
, 2008
"... We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Diractype equations with the ..."
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Cited by 28 (8 self)
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We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Diractype equations
Some Sharp L² Inequalities for Dirac Type Operators
, 2007
"... We use the spectra of Dirac type operators on the sphere S n to produce sharp L² inequalities on the sphere. These operators include the Dirac operator on S n, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for ..."
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We use the spectra of Dirac type operators on the sphere S n to produce sharp L² inequalities on the sphere. These operators include the Dirac operator on S n, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities
Results 1  10
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51,850