相关论文: Dirac reduction revisited
This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein…
We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.
In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a…
The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional…
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian…
In this article, we survey the recent constructions of cyclic cocycles on the Harish-Chandra Schwartz algebra of a connected real reductive Lie group $G$ and their applications to higher index theory for proper cocompact $G$-actions.
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\in\Lambda^3M$ by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac…
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the…
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential…
The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge…
Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
We extend known prequantization procedures for Poisson and presymplectic manifolds by defining the prequantization of a Dirac manifold P as a principal U(1)-bundle Q with a compatible Dirac-Jacobi structure. We study the action of Poisson…
We study reduction of Dirac structures from the point of view of pure spinors. We describe explicitly the pure spinor line bundle of the reduced Dirac structure. We also obtain results on reduction of generalized Calabi-Yau structures.
A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the…
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
We show that in modified Faddeev-Jackiw formalism, first and second class constraints appear at each level, and the whole constraint structure is in exact correspondence with level by level method of Dirac formalism.