共查询到20条相似文献,搜索用时 0 毫秒
1.
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones, we propose a new twisted reality condition for the Dirac operator. 相似文献
2.
Jonathan Dimock 《Letters in Mathematical Physics》2011,98(2):157-166
We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment
employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard
Fock space construction. 相似文献
3.
Simon Raulot 《Communications in Mathematical Physics》2013,318(2):411-427
We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for surfaces with constant mean curvature vector field in Minkowski space. 相似文献
4.
Petr Šeba 《Letters in Mathematical Physics》1988,16(1):51-59
The method of complex scaling, usually used in atomic and molecular resonance calculations, is generalized to the Dirac equation. It is shown that Dirac resonances are associated with nonreal eigenvalues of the scaled Dirac Hamiltonian. The perturbation theory for the resonance parameters is also discussed. 相似文献
5.
Daniel S. Freed Gregory W. Moore Graeme Segal 《Communications in Mathematical Physics》2007,271(1):247-274
In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that
magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo
torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized
by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is -graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field
in string theory, showing that its K-theory class cannot be measured. 相似文献
6.
We find sufficient conditions for the absence of harmonic L 2 spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi?inescu and the second author. 相似文献
7.
We investigate parallel spinors on the Eguchi–Hanson metrics and find the space of complex parallel spinors is complex two-dimensional. For the metrics of Eguchi–Hanson type with the zero scalar curvature, we separate variables for the harmonic spinors and obtain the solutions explicitly. 相似文献
8.
Alain Bachelot 《Communications in Mathematical Physics》2008,283(1):127-167
We investigate the global solutions of the Dirac equation on the Anti- de-Sitter Universe. Since this space is not globally
hyperbolic, the Cauchy problem is not, a priori, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio
beween the mass M of the field and the cosmological constant Λ > 0: it appears a critical value, Λ/12, which plays a role similar to the Breitenlohner-Freedman
bound for the scalar fields. When M
2 ≥ Λ/12 there exists a unique unitary dynamics. On the contrary, for the light fermions satisfying M
2 < Λ/12, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases,
the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy. 相似文献
9.
Based on the method oftransformation operators, the Darboux transformation operator has been constructed for the one-dimensional stationary Dirac equation. The properties of this operator have been studied. As an application, exactly solvable transparent potentials and potentials with the spectrum of a relativistic harmonic oscillator have been obtained. 相似文献
10.
Florian Hanisch Frank Pf?ffle Christoph A. Stephan 《Communications in Mathematical Physics》2010,300(3):877-888
We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with
totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the Riemann
curvature tensor. Finally we deduce the Lagrangian for the Standard Model of particle physics in the presence of torsion from
the Chamseddine-Connes Dirac operator. 相似文献
11.
We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operators for different energy levels for this system are obtained. 相似文献
12.
Hessel Posthuma 《Letters in Mathematical Physics》2011,95(1):89-107
Using a coset version of the cubic Dirac operators for affine Lie algebras, we give an algebraic construction of the Dirac
induction homomorphism for loop group representations. With this, we prove a homogeneous generalization of the Weyl–Kac character
formula and show compatibility with Dirac induction for compact Lie groups. 相似文献
13.
《Nuclear Physics A》1987,467(4):717-743
The effects of polarization of the Dirac sea on finite solitons in a simple theory in which fermions interact with a single scalar field are studied. The mass shift for a given background scalar field is computed numerically and compared to approximations arising from expansions in inverse powers of the effective fermion mass and in powers of derivatives of the background scalar field. The conditions under which such approximations succeed are discussed. When such approximations work one can derive local equations of motion for the soliton fields which include the effects of polarizing the Dirac sea. These new equations are studied and energy minimization is used to explore the effects of the Dirac sea on the structure of the soliton. Calculations for a typical Friedberg-Lee soliton are presented, and it is shown that, while the approximations do not work well for fields employed to model the quark structure of nucleons, they do provide an upper bound for the mass of the soliton. A scalar field typical of those used to model 16O in quantum hadrodynamics is also studied, and it is shown that, when the effective potential is supplemented by the next term occurring in a derivative expansion, the renormalized shift in the energy of the Dirac sea is well approximated. 相似文献
14.
15.
We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operaors for different energy levelsfor this system are obtained. 相似文献
16.
Frank Pfffle 《Journal of Geometry and Physics》2000,35(4):1189
The Dirac spectra and the eta invariants of three-dimensional Bieberbach manifolds are computed. Compact connected three-dimensional spin manifolds admitting parallel non-vanishing spinors are identified as flat tori. 相似文献
17.
Expressions of the S-matrix, for the Dirac case, which are suitable for analytic continuation over the complex k-plane for a large class of potentials, fulfilling conditions (1), are derived. 相似文献
18.
Dierck-Ekkehard Liebscher 《Annalen der Physik》1985,497(1):35-40
We discuss the problem of the derivation and the interpretation of metric tensors and generalized equations of motion for test particles from quasilinear spinor equations. 相似文献
19.
Within the framework of a program of the construction (derivation) of the classical space-time from a certain system of notions and relations (binary systems of complex relations) that show up in microcosm physics, the prototype of the Dirac equation for a free particle is considered, and the change from this prototype to the Dirac equation is followed first in the momentum and then in the coordinate representation. The procedure of changing from elementary bases to a macroinstrument in reference to which the generally accepted physical notions are formulated. 相似文献
20.
Using the correspondence between the Clifford and exterior algebras we write the Dirac equation in terms of differential forms. The covariances of the theory are then examined. We show in detail the correspondence with usual matrix methods. 相似文献