Some essentially self-adjoint Dirac type operators,II (resolvent estimates near infinity)

We obtain norm estimates for the resolvent of the Dirac operator. These estimates verify the key assumptions of an extended version of the Rellich-Kato theorem concerning essential self-adjointness. The application of this abstract theorem then shows that the one-electron Dirac operator can admit a Coulomb potential, for atomic numbers less than or equal to 118, plus a second perturbation which satisfies a mild Stummel type bound, and remain essentially self-adjoint.     

Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators

Distinguished self-adjoint extensions of Dirac operators are characterized by Nenciu and constructed by means of cut-off potentials by Wüst. In this paper it is shown that the existence and a more explicit characterization of Nenciu's self-adjoint extensions can be obtained as a consequence from results of the cut-off method, that these extensions are the same as the extensions constructed with cut-off potentials and that they are unique in some sense.On leave from Universität Zürich, Schöneberggasse 9, CH-8001 Zürich. Supported by Swiss National Science FoundationOn leave from Technische Universität Berlin, Straße des 17. Juni 135, D-1000 Berlin     

Yet another formulation of the Dirac equation

The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors and *_µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain .     

Local nets and self-adjoint extensions of quantum field operators

We consider Wightman fields having the property that some closed extensions of the field operators generate locally commuting von Neumann algebras. We show that for such fields the hermitian field operators have self-adjoint extensions, possibly in an enlarged Hilbert space, such that bounded functions of the self-adjoint operators commute locally.     

Constructing quantum observables and self-adjoint extensions of symmetric operators. II. Differential operators

We discuss a problem of constructing self-adjoint ordinary differential operators starting from self-adjoint differential expressions based on the general theory of self-adjoint extensions of symmetric operators outlined in [1]. We describe one of the possible ways of constructing in terms of the closure of an initial symmetric operator associated with a given differential expression and deficient spaces. Particular attention is focused on the features peculiar to differential operators, among them on the notion of natural domain and the representation of asymmetry forms generated by adjoint operators in terms of boundary forms. Main assertions are illustrated in detail by simple examples of quantum-mechanical operators like the momentum or Hamiltonian. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 3–36, August, 2007.     

A priori estimates for the Hill and Dirac operators

The Hill operator Ty = −y″ + q′(t)y is considered in L ²(ℝ), where q ∈ L ²(0, 1) is a periodic real potential. The spectrum of T is absolutely continuous and consists of bands separated by gaps. We obtain a priori estimates of gap lengths, effective masses, and action variables for the KDV equation. In the proof of these results, the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator is used. Similar estimates for the Dirac operator are obtained.     

Relativistic extension of the Hohenberg-Kohn theorem

Using the configuration-space HamiltonianH ₊ which is derivable within the framework of quantum electrodynamics, we extend the Hohenberg-Kohn theorem to the relativistic theory of electrons in atoms or molecules.     

Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting, we establish the existence and asymptotics of weakly coupled eigenvalues and Lieb–Thirring inequalities. As physical applications, we investigate the damped wave equation and armchair graphene nanoribbons.     

On the algebra of symmetries of Laplace and Dirac operators

We consider a generalization of the classical Laplace operator, which includes the Laplace–Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like operator, we determine a set of symmetries commuting with it, in the form of generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplace-like operator. We explicitly determine a family of graded operators which commute or anticommute with our Dirac-like operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higher-rank Bannai–Ito algebra.     

i(h-) (a-at)是算符吗

指出将ｉｈδ／δｔ作为算符来讨论没有多大意义,且ｉｈδ／δｔ≠Ｈ,△ｔ△Ｅ≥ｈ／２不可能通过ｔ与ｉｈδ／δｔ或ｔ与Ｈ的对易关系得出。     

An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work.     

Superspace formulation of the dynamical symmetries of the Dirac magnetic monopole

The superspace formulation for the dynamical supersymmetry of the Pauli system in the presence of a Dirac magnetic monopole is presented. It is used to prove that Osp(1, 1) is the largest dynamical invariance group of this system. The action of finite transformations on the parameters of superspace and on the supervariables is given.     

Some Studies of the Neutron's Dirac Equation

In this paper, we continue the discussion for the neutron's Dirac equation and relevant problems after Ref.[1]. We consider the neutron's Dirac equation with the electric moment besides the magnetic moment, solve rigorously the neutron's Dirac equation in a uniform electromagnetic field. We also set up a relativistic neutron's spin-echo theory with a magnetic moment.     

Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem

Fermionic quantization, or Clifford algebra, is combined with pseudodifferential operators to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold.