48 research outputs found
The general dielectric tensor for bi-kappa magnetized plasmas
In this paper we derive the dielectric tensor for a plasma containing
particles described by an anisotropic superthermal (bi-kappa) velocity
distribution function. The tensor components are written in terms of the
two-variables kappa plasma special functions, recently defined by Gaelzer and
Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new
mathematical properties for these functions, which are useful for the
analytical treatment, numerical implementation and evaluation of the functions
and, consequently, of the dielectric tensor. The formalism developed here and
in the previous paper provides a mathematical framework for the study of
electromagnetic waves propagating at arbitrary angles and polarizations in a
superthermal plasma.Comment: Accepted for publication in Physics of Plasma
Obliquely propagating electromagnetic waves in magnetized kappa plasmas
Velocity distribution functions (VDFs) that exhibit a power-law dependence on
the high-energy tail have been the subject of intense research by the plasma
physics community. Such functions, known as kappa or superthermal
distributions, have been found to provide a better fitting to the VDFs measured
by spacecraft in the solar wind. One of the problems that is being addressed on
this new light is the temperature anisotropy of solar wind protons and
electrons. In the literature, the general treatment for waves excited by
(bi-)Maxwellian plasmas is well-established. However, for kappa distributions,
the wave characteristics have been studied mostly for the limiting cases of
purely parallel or perpendicular propagation, relative to the ambient magnetic
field. Contributions to the general case of obliquely-propagating
electromagnetic waves have been scarcely reported so far. The absence of a
general treatment prevents a complete analysis of the wave-particle interaction
in kappa plasmas, since some instabilities can operate simultaneously both in
the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J.
Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor
and dispersion relations for the low-frequency, quasi-perpendicular dispersive
Alfv\'en waves resulting from a kappa VDF. In the present work, the formalism
introduced by Ref. 1 is generalized for the general case of electrostatic
and/or electromagnetic waves propagating in a kappa plasma in any frequency
range and for arbitrary angles. An isotropic distribution is considered, but
the methods used here can be easily applied to more general anisotropic
distributions, such as the bi-kappa or product-bi-kappa.Comment: Accepted for publication in Physics of Plasmas; added references for
section
On time-dependent AdS/CFT
We clarify aspects of the holographic AdS/CFT correspondence that are typical
of Lorentzian signature, to lay the foundation for a treatment of
time-dependent gravity and conformal field theory phenomena. We provide a
derivation of bulk-to-boundary propagators associated to advanced, retarded and
Feynman bulk propagators, and provide a better understanding of the boundary
conditions satisfied by the bulk fields at the horizon. We interpret the
subleading behavior of the wavefunctions in terms of specific vacuum
expectation values, and compute two-point functions in our framework. We
connect our bulk methods to the closed time path formalism in the boundary
field theory.Comment: 19 pages, v2: added reference, JHEP versio
Exact quantization of a PT-symmetric (reversible) Li\'enard-type nonlinear oscillator
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard
type one dimensional nonlinear oscillator both semiclassically and quantum
mechanically. The associated time independent classical Hamiltonian is of
non-standard type and is invariant under a combined coordinate reflection and
time reversal transformation. We use von Roos symmetric ordering procedure to
write down the appropriate quantum Hamiltonian. While the quantum problem
cannot be tackled in coordinate space, we show how the problem can be
successfully solved in momentum space by solving the underlying Schr\"{o}dinger
equation therein. We obtain explicitly the eigenvalues and eigenfunctions (in
momentum space) and deduce the remarkable result that the spectrum agrees
exactly with that of the linear harmonic oscillator, which is also confirmed by
a semiclassical modified Bohr-Sommerfeld quantization rule, while the
eigenfunctions are completely different.Comment: 10 pages, 1 figure, Fast Track Communicatio
Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory
On Nonperturbative Calculations in Quantum Electrodynamics
A new approach to nonperturbative calculations in quantum electrodynamics is
proposed. The approach is based on a regular iteration scheme for solution of
Schwinger-Dyson equations for generating functional of Green functions. The
approach allows one to take into account the gauge invariance conditions (Ward
identities) and to perform the renormalization program. The iteration scheme
can be realized in two versions. The first one ("perturbative vacuum")
corresponds to chain summation in the diagram language. In this version in
four-dimensional theory the non-physical singularity (Landau pole) arises which
leads to the triviality of the renormalized theory. The second version
("nonperturbative vacuum") corresponds to ladder summation and permits one to
make non-perturbative calculations of physical quantities in spite of the
triviality problem. For chiral-symmetrical leading approximation two terms of
the expansion of the first-step vertex function over photon momentum are
calculated. A formula for anomalous magnetic moment is obtained. A problem of
dynamical chiral symmetry breaking (DCSB) is considered, the calculations are
performed for renormalized theory in Minkowsky space. In the strong coupling
region DCSB-solutions arise. For the renormalized theory a DCSB-solution is
also possible in the weak coupling region but with a subsidiary condition on
the value of .Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion
and refs. are adde
Gauge-invariant quantum gravitational corrections to correlation functions
A recent proposal for gauge-invariant observables in inflation [R. Brunetti et al., JHEP 1608 (2016) 032] is examined. We give a generalisation of their construction to general background spacetimes. In flat space, we calculate one-loop graviton corrections to a scalar two-point function in a general gauge for the graviton. We explicitely show how the gauge-dependent terms cancel between the usual self-energy contributions and the additional corrections inherent in these observables. The one-loop corrections have the expected functional form, contrary to another recently studied proposal for gauge-invariant observables [M. B. Fröb, Class. Quant. Grav. 35 (2018) 035005] where this is not the case. Furthermore, we determine the one-loop graviton corrections to the four-point coupling of the gauge-invariant scalar field, and the corresponding running of the coupling constant induced by graviton loops. Interestingly, the β function is negative for all values of the non-minimal coupling of the scalar field to curvature