共查询到20条相似文献,搜索用时 15 毫秒
1.
Stability and instability of relativistic electrons in classical electromagnetic fields 总被引:3,自引:0,他引:3
Elliott H. Lieb Heinz Siedentop Jan Philip Solovej 《Journal of statistical physics》1997,89(1-2):37-59
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons
given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary classical magnetic
field of finite energy. Despite the previously known facts that ordinary nonrelativistic matter with magnetic fields, or relativistic
matter without magnetic fields, is already unstable when a, the fine structure constant, is too large, it is noteworthy that
the combination of the two is still stableprovided the projection onto the positive energy states of the Dirac operator, whichdefines the electron, is chosen properly. A good choice is to include the magnetic field in the definition. A bad choice, which always
leads to instability, is the usual one in which the positive energy states are defined by the free Dirac operator. Both assertions
are proved here.
This paper is dedicated to Bernard Jancovici on the occasion of his 65th birthday. 相似文献
2.
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. We do that for the standard version of the gravitational Dirac equation, and for two alternative equations based on the tensor representation of the Dirac fields. The latter equations may be defined when the spacetime is four‐dimensional, noncompact, and admits a spinor structure. We find that, for each among the three versions of the equation, the vast majority of the possible coefficient changes do not lead to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. In particular, we prove that the Dirac energy spectrum is not unique. This non‐uniqueness of the energy spectrum comes from an effect of the choice of coefficients, and applies in any given coordinates. 相似文献
3.
V. V. Varlamov 《International Journal of Theoretical Physics》2016,55(11):5008-5045
Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations). All these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type (l, 0) ⊕ (0, l), where l is a spin value, whereas for arbitrary spin chains we have degenerate spectrum. Energy spectra of the stability levels (electron and proton states) of the matter spectrum are studied in detail. It is shown that these stability levels have a nature of threshold scales of the fractal structure associated with the system of interlocking representations of the Lorentz group. 相似文献
4.
《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
5.
The gravitating matter is studied within the framework of noncommutative geometry. The noncommutative Einstein-Hilbert action
on the product of a four-dimensional manifold with discrete space gives models of matter fields coupled to the standard Einstein
gravity. The matter multiplet is encoded in the Dirac operator which yields a representation of the algebra of universal forms.
The general form of the Dirac operator depends on a choice of the grading of the corresponding spinor bundle. A choice is
given, which leads to the nonlinear vectorσ-model coupled to the Einstein gravity. 相似文献
6.
Yu. I. Klimenko 《Russian Physics Journal》1974,17(11):1481-1485
A covariant spin operator is found for fermions with anomalous magnetic and electric dipole moments in constant external fields. The spin behavior of a neutral fermion in constant magnetic and electric fields is investigated using exact solutions obtained for the Dirac equation. 相似文献
7.
《Physics letters. [Part B]》1988,206(4):579-583
We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. 相似文献
8.
The Dirac oscillator was initially introduced as a Dirac operator which is linear in momentum and coordinate variables. In contrast to the usual 2D Dirac oscillator, the 2D Kramers–Dirac oscillator admits the time-reversal symmetry, which is a reason for the present nomenclature. It is shown that there exists a family of eigenstates associated with an eigenvalue linear in the control parameter, and the eigenvalue in question goes down from positive values to negative values as the parameter varies in the positive direction. The other eigenvalues are broken up into two bands, positive and negative. The 2D Dirac and the 2D Kramers–Dirac oscillators are compared in their physical grounds and in their spectral structure from the viewpoint of the time-reversal symmetry. 相似文献
9.
The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. Bounds on the sum of the negative eigenvalues are called magnetic Lieb–Thirring (MLT) inequalities. The purpose of this paper is twofold. First, we prove a new MLT inequality in a simple way. Second, we give a short summary of our recent proof of a more refined MLT inequality(8) and we explain the differences between the two results and methods. The main feature of both estimates, compared to earlier results, is that in the large field regime they grow with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain optimal upper bounds on the pointwise density of zero energy eigenfunctions of the Dirac operator. 相似文献
10.
11.
12.
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best constant as in the free case. This leaves naturally open an interesting question whether there exist magnetic fields for which a Hardy inequality with a better constant than the usual one, in connection with the well known diamagnetic phenomenon arising in non-relativistic models. 相似文献
13.
The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force. 相似文献
14.
《Physics letters. [Part B]》1988,208(1):8-14
The longitudinal response function for quasielastic electron scattering from nuclear matter is calculated in a relativistic random phase approximation to the Walecka model including vacuum polarization effects. The Walecka model has nucleons interacting with isoscalar sigma and omega meson fields. The change in the vacuum polarization response of the Dirac sea because of the decrease in the relativistic effective mass of the nucleons leads to a thirty percent decrease in the energy integrated longitudinal response function (Coulomb sum rule). This change is isoscalar. Therefore, the transverse response, which is dominated by the isovector anomalous moment, is largely unchanged. 相似文献
15.
L. Bugliaro J. Fröhlich G.M. Graf J. Stubbe C. Fefferman 《Communications in Mathematical Physics》1997,187(3):567-582
A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an
effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter
in magnetic fields is given.
Received: 19 September 1996 / Accepted: 3 January 1997 相似文献
16.
The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein–Yang–Mills
background fields with a half-integer Chern–Simons number. The proof holds for any gauge group and applies to Dirac spinors
in an arbitrary representation of the gauge group. The class of background fields contains all regular, asymptotically flat,
CP-symmetric configurations with a connection that is globally described by a time-independent spatial one-form which vanishes
sufficiently fast at infinity. A subset is provided by all neutral, spherically symmetric configurations which satisfy a certain
genericity condition, and for which the gauge potential is purely magnetic with real magnetic amplitudes.
Received: 19 March 1997 / Accepted: 21 April 1997 相似文献
17.
18.
19.
We have studied the tunneling of Dirac fermions through magnetic barriers in graphene. Magnetic barriers are produced via delta function-like inhomogeneous magnetic fields in which Dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to Klein paradox caused by electrostatic barriers. The transmission through the magnetic barriers as functions of incident energy and angle of incoming fermions shows characteristic oscillations associated with tunneling resonances. We have also found the confined states in the magnetic barrier region which turn out to correspond to the total internal reflection in the usual optics. 相似文献
20.
Dali Wang 《Physics letters. A》2009,373(44):4082-4085
We investigate the magnetically confined states of the massless Dirac fermions in a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the dot. The calculated energy spectrum exhibits quite different features with and without the magnetic field inside the dot. It is found that the degeneracy of the relativistic Landau level with negative angular momenta can be lifted, and this degeneracy breaking can be modulated by the magnetic field inside the dot. Moreover, such a system can form the strongly localized states within the dot and along its boundary, especially with the magnetic field inside the dot. 相似文献