Spinor Green Research Articles

Spinor Green’s functions via spherical means on products of space forms

We explicitly compute the Green’s function of the spinor Klein–Gordon equation on the Riemannian and Lorentzian manifolds of the form M 0 × ⋯ × M N , with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions.

Spinor Green function in higher-dimensional cosmic string space-time in the presence of magnetic flux

In this paper we investigate the vacuum polarization effects associated with quantum fermionic charged fields in a generalized $(d+1)-$dimensional cosmic string space-times considering the presence of a magnetic flux along the string. In order to develop this analysis we calculate a general expression for the respective Green function, valid for several different values of $d$, which is expressed in terms of a bispinor associated with the square of the Dirac operator. Adopting this result, we explicitly calculate the renormalized vacuum expectation values of the energy-momentum tensors, $ _{Ren.}$, associated with massless fields. Moreover, for specific values of the parameters which codify the cosmic string and the fractional part of the ratio of the magnetic flux by the quantum one, we were able to present in closed forms the bispinor and the respective Green function for massive fields.

Josephson current in superconductor/ferromagnet/ superconductor junctions

The Bogoliubov-de Gennes equation and Nambu spinor Green's function approach are applied to studying the Josephson current in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions in the clean limit. It is found that the critical current exhibits a damped oscillation with the F thickness d, the oscillation period equal to 2πξF with ξF the coherence length of the F. The change of the critical current from positive to negative is determined by factor cosφ′ with φ′=d/ξF as the F-induced phase difference. The exponent decay of the critical current is close related to that of the superconductor order parameter in the F, both of them having the same decay length.

Orientation dependence of proximity effect in ferromagnet/$\mathsf{d}$-wave superconductor junctions

The Nambu spinor Green’s function approach is applied to studying the proximity effect in ferromagnet/d-wave superconductor (FM/d-wave SC) junctions. It is found that the magnitude of the proximity effect depends to a great extent on the orientation of the SC crystal with respect to the interface normal. On the FM side, near the interface there are two different types of density of states (DOS) with superconducting features. On the SC side, the DOS near the interface is spin dependent, indicating a local coexistence of weak ferromagnetism and d-wave superconductivity.

VACUUM POLARIZATION OF A CHARGED MASSLESS FERMIONIC FIELD BY A MAGNETIC FLUX IN THE COSMIC STRING SPACETIME

We calculate the vacuum averages of the energy–momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: (i) a homogeneous field inside the tube, (ii) a magnetic field proportional to 1/r, and (iii) a cylindrical shell with δ-function. In these three cases the axis of the infinitely long tubes of radius R coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e. corresponding to the spinor Green's functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy–momentum tensor.

Proximity effects in ferromagnet/superconductor structures

The Nambu spinor Green’s function approach is applied to study proximity effects in ferromagnet/superconductor (FM/SC) structures. They include the induced superconducting order parameter and density of states (DOS) with superconducting feature on the FM side, and spin-dependent DOS within the energy gap on the SC side. The latter indicates an appearance of gapless superconductivity and a coexistence of ferromagnetism and superconductivity in a small regime near the interface. The influence of exchange energy in FM and barrier strength at interface on the proximity effects is discussed.

Coexistence of superconductivity and ferromagnetism in ferromagnet/superconductor proximity structures

The Nambu spinor Green's function approach is applied to calculating the density of states (DOS) and superconducting order parameter in normal-metal/insulator/ferromagnet/superconductor (NM/I/FM/SC) junctions. It is found that the s-wave superconductivity and ferromagnetism can coexist near the FM/SC interface, which is induced by proximity effect. On the SC side, the spin-dependent DOS appears both within and without the energy gap. On the FM side, the superconducting order parameter displays a damped oscillation and the DOS exhibits some superconducting behavior. The calculated result for the DOS in FM for “0 state” and “π state” can reproduce recent tunneling spectra in Al/Al2O3/PdNi/Nb tunnel junctions.

Gapless superconductivity in ferromagnet/superconductor junctions

The Nambu spinor Green's function approach is applied to study the proximity effect in ferromagnet/superconductor (FM/SC) junctions. It is found that gapless superconductivity appears in both FM and SC regions near the FM/SC interface. In FM the superconducting order parameter induced by the proximity effect displays a damped oscillation. When the distance from the interface increased, following a transition from the ``0 state'' to the $``\ensuremath{\pi}$ state,'' the induced superconducting density of states in FM is flipped with respect to the normal state. Quantitative agreement is obtained between the calculated results and recent tunneling spectra in $\mathrm{Al}/{\mathrm{Al}}_{2}{\mathrm{O}}_{3}/\mathrm{PbNi}/\mathrm{Nb}$ tunnel junctions. In particular, peak and dip behavior of the induced superconducting DOS in FM is well reproduced.

Euclidean thermal spinor Green's function in the spacetime of a straight cosmic string

Within the framework of the quantum field theory at finite temperature on a conical space, we determine the Euclidean thermal spinor Green's function for a massless spinor field. We then calculate the thermal average of the energy - momentum tensor of a thermal bath of massless fermions. In the high-temperature limit, we find that the straight cosmic string does not perturb the thermal bath.

Euclidean spinor Green’s functions in the space–time of a straight cosmic string

The spinor Green’s function and the twisted spinor Green’s function in a Euclidean space with a conical-type line singularity are generally determined. In particular, in the neighborhood of the point source, they are expressed as a sum of the usual Euclidean spinor Green’s function and a regular term. In four dimensions, these determinations can be used to calculate the vacuum energy density and the twisted one for a massless spinor field in the space–time of a straight cosmic string. In the Minkowski space–time, the vacuum energy density for a massive twisted spinor field is explicitly determined.

Exact and approximate fermion Green's functions in QED and QCD.

That special variant of the Fradkin representation, previously defined for scalar Green's functions ${\mathit{G}}_{\mathit{c}}$(x,y\ensuremath{\Vert}A) in an arbitrary potential A(z), is here extended to the case of vector interactions and spinor Green's functions of QED and QCD. An exact representation is given which may again be approximated by a finite number N of quadratures, with the order of magnitude of the errors generated specified in advance, and decreasing with increasing N. A feature appears for both exact and approximate ${\mathit{G}}_{\mathit{c}}$[A]: the possibility of chaotic behavior of a function central to the representation, which in turn generates chaotic behavior in ${\mathit{G}}_{\mathit{c}}$[A] for certain A(z). An example is given to show how the general criterion specified here works for a known case of ``quantum chaos,'' in a potential theory context of first quantization. When the full, nonperturbative, radiative corrections of quantum field theory are included, such chaotic effects are removed.

Quantized Dirac field in curved Riemann-Cartan background. I. Symmetry properties, Green's function

In the present series of papers, we study the properties of quantized Dirac field in curved Riemann-Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann-Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann-Cartan background, using the Schwinger-DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background.