共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate η-invariants and prove an APS theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities. 相似文献
2.
Constantine Callias 《Communications in Mathematical Physics》1978,62(3):213-234
Using an approach inspired by the theory of the anomalous divergence of the axial vector current, we derive trace formulas for the resolvents of Dirac operators on open spaces of odd dimension. These formulas readily yield index theorems for these operators. As applications we determine the index of the Dirac operator for a particle of arbitrary isospin in the background field of a static system of SU(2) monopoles; and we find formulas in essentially closed form for certain determinants involving these operators.This work is supported in part through funds provided by the U.S. Department of Energy (DOE) under contract EY-76-C-02-3069 相似文献
3.
John Lott 《Communications in Mathematical Physics》2002,230(1):41-69
In the first part of this paper, given a smooth family of Dirac-type operators on an odd-dimensional closed manifold, we
construct an abelian gerbe-with-connection whose curvature is the three-form component of the Atiyah-Singer families index
theorem. In the second part of the paper, given a smooth family of Dirac-type operators whose index lies in the subspace of the reduced K-theory of the parametrizing space, we construct a set of Deligne cohomology classes of degree i whose curvatures are the i-form component of the Atiyah-Singer families index theorem.
Received: 27 September 2001 / Accepted: 5 April 2002 Published online: 22 August 2002 相似文献
4.
S. N. M. Ruijsenaars 《Communications in Mathematical Physics》1989,124(4):553-593
The kernels of operators associated with special chiral gauge transformations (kinks) in the 2N-dimensional Dirac theory are explicitly determined. The result is used to obtain index formulas for Fredholm operators corresponding to continuous chiral gauge transformations. Moreover, the Fock space quadratic forms corresponding to the kinks are proved to converge to the Dirac field as the kink size goes to zero. It is also shown that forN 1, 2(mod 4) the Majorana field can be reached in a similar fashion.Work supported by the Netherlands Organisation for the Advancement of Research (NWO) 相似文献
5.
In this paper, we construct the Quillen metric on the determinant bundle associated with a family of elliptic first order differential operators. We also introduce a unitary connection on and calculate its curvature. Our results will be applied to the case of Dirac operators in a forthcoming paper. 相似文献
6.
Arthur Jaffe Andrzej Lesniewski Jonathan Weitsman 《Communications in Mathematical Physics》1988,114(1):147-165
We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper [1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one [2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow 相似文献
7.
In anomaly-free quantum field theories the integrand in the bosonic functional integral—the exponential of the effective action
after integrating out fermions—is often defined only up to a phase without an additional choice. We term this choice ``setting
the quantum integrand'. In the low-energy approximation to M-theory the E8-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent
interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand
of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions.
In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction
of heterotic M-theory on cylinders.
The work of D.F. is supported in part by NSF grant DMS-0305505. The work of G.M. is supported in part by DOE grant DE-FG02-96ER40949 相似文献
8.
Paolo Piazza 《Communications in Mathematical Physics》1996,178(3):597-626
We define determinant bundles associated to the following data: (i) a family of generalized Dirac operators on even dimensional manifolds with boundary, (ii) the choice of a spectral section for the family of Dirac operators induced on the boundary. Under the assumption that the operators of the boundary family have null spaces of constant dimension we define, through the notion ofb-zeta function, a Quillen metric. We also introduce the analogue of the Bismut-Freed connection. We prove that the curvature of a natural perturbation of the Bismut-Freed connection equals the 2-form piece in the right-hand side of the family index formula, thus extending to manifolds with boundary results of Quillen, Bismut and Freed. Given a closed fibration, we investigate the behaviour of the Quillen metric and of the Bismut-Freed connection under the operation of surgery along a fibering hypersurface. We prove, in particular, additivity formulae for the curvature and for the logarithm of the holonomy. 相似文献
9.
Koji Hasegawa 《Communications in Mathematical Physics》1997,187(2):289-325
For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on
the type A weight space. According to the fundamental relation RLL=LLR, taking the trace of the L-operator gives a set of commuting difference operators. We show that for the above mentioned L-operator
this approach gives Macdonald type operators with elliptic theta function coefficient, actually equivalent to Ruijsenaars'
operators. The relationship between the difference L-operator and Krichever's Lax matrix is given, and an explicit formula
for elliptic commuting differential operators is derived. We also study the invariant subspace for the system which is spanned
by symmetric theta functions on the weight space.
Received: 27 December 1995 / Accepted: 11 November 1996 相似文献
10.
Paolo Piazza 《Communications in Mathematical Physics》1998,193(1):105-124
Let be a closed fibration of Riemannian manifolds and let , be a family of generalized Dirac operators. Let be an embedded hypersurface fibering over B; . Let be the Dirac family induced on . Each fiber in is the union along of two manifolds with boundary . In this paper, generalizing our previous work[16], we prove general surgery rules for the local and global anomalies of the Bismut–Freed connection on the determinant bundle associated to . Our results depend heavily on the b-calculus [12], on the surgery calculus [11] and on the APS family index theory developed in [13], in particular on the notion
of spectral section for the family .
Received: 23 October 1996 / Accepted: 28 July 1997 相似文献
11.
For a compact group G of symplectomorphisms we define a G-trace on the algebra of quantum observables by postulating its properties. We give an explicit construction of such a trace and prove a G-index theorem similar to the Atiyah–Segal–Singer equivariant index theorem for elliptic operators. 相似文献
12.
Nikhil Savale 《Communications in Mathematical Physics》2014,332(2):847-884
We prove an asymptotic bound on the eta invariant of a family of coupled Dirac operators on an odd dimensional manifold. In the case when the manifold is the unit circle bundle of a positive line bundle over a complex manifold, we obtain precise formulas for the eta invariant. 相似文献
13.
V. Dmitrašinović Hua-Xing Chen 《The European Physical Journal C - Particles and Fields》2011,71(2):1543
We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good
isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon
operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin
Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent
baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties
of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with
given values of spin (Lorentz group representation), chiral symmetry (U
L
(2)×U
R
(2) group representation) and isospin appropriate for the first angular excited states of the nucleon. 相似文献
14.
Boris Feigin Michio Jimbo Tetsuji Miwa Alexandr Odesskii Yaroslav Pugai 《Communications in Mathematical Physics》1998,191(3):501-541
We construct a family of intertwining operators (screening operators) between various Fock space modules over the deformed
W
n
algebra. They are given as integrals involving a product of screening currents and elliptic theta functions. We derive a
set of quadratic relations among the screening operators, and use them to construct a Felder-type complex in the case of the
deformed W
3 algebra.
Received: 3 March 1997 / Accepted: 20 May 1997 相似文献
15.
It is shown that the N = 4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant constant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N = 4 supersymmetry. 相似文献
16.
For a product family of Weyl operators of possibly non-zero index on a compact manifoldX, we express parallel transport in the determinant line bundle in terms of the spectral asymmetry of a Dirac operator on ×X. This generalizes the results of [7], where we dealt only with invertible operators.Supported in part by NSF Grant No. PHY 8605978 and the Robert A. Welch FoundationSupported in part by NSF Grant No. PHY 8215249 相似文献
17.
Adams DH 《Physical review letters》2001,86(2):200-203
In the continuum, a topological obstruction to the vanishing of the non-Abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. This involves deriving an index theorem for a family of lattice Dirac operators satisfying the Ginsparg-Wilson relation. The index density is proportional to Lüscher's topological field in 2n+2 dimensions. 相似文献
18.
We construct noncommutative principal fibrations Sθ7→Sθ4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. “The algebra inclusion is an example of a not-trivial quantum principal bundle.” 相似文献
19.
By using the elliptic analogue of the Drinfeld currents in the elliptic algebra
, we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group . For this purpose, we introduce a set of new currents in . As in the N=2 case, we find a structure of as a certain tensor product of and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in . Using the coalgebra structure of and the above tensor structure, we derive a free field realization of the -analogue of -intertwining operators. The resultant operators coincide with those of the vertex operators in the -type face model. 相似文献
20.
We construct open sets of C
k
(k ≥ 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay
of correlations with respect to the unique physical measure. 相似文献