42,523 research outputs found
Green function for hyperbolic media
We revisit the problem of the electromagnetic Green function for homogeneous
hyperbolic media, where longitudinal and transverse components of the
dielectric permittivity tensor have different signs. We analyze the dipole
emission patterns for both dipole orientations with respect to the symmetry
axis and for different signs of dielectric constants, and show that the
emission pattern is highly anisotropic and has a characteristic cross-like
shape: the waves are propagating within a certain cone and are evanescent
outside this cone. We demonstrate the coexistence of the cone-like pattern due
to emission of the extraordinary TM-polarized waves and elliptical pattern due
to emission of ordinary TE-polarized waves. We find a singular complex term in
the Green function, proportional to the function and governing the
photonic density of states and Purcell effect in hyperbolic media.Comment: 10 pages, 7 figure
Worldline Green Functions for Arbitrary Feynman Diagrams
We propose a general method to obtain the scalar worldline Green function on
an arbitrary 1D topological space, with which the first-quantized method of
evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary
ones. The electric analog of the worldline Green function problem is found and
a compact expression for the worldline Green function is given, which has
similar structure to the 2D bosonic Green function of the closed bosonic
string.Comment: 20 pages, 6 figures; v2: typos corrected, references adde
On gauge-invariant Green function in 2+1 dimensional QED
Both the gauge-invariant fermion Green function and gauge-dependent
conventional Green function in dimensional QED are studied in the large
limit. In temporal gauge, the infra-red divergence of gauge-dependent
Green function is found to be regulariable, the anomalous dimension is found to
be . This anomalous dimension was argued to be
the same as that of gauge-invariant Green function. However, in Coulomb gauge,
the infra-red divergence of the gauge-dependent Green function is found to be
un-regulariable, anomalous dimension is even not defined, but the infra-red
divergence is shown to be cancelled in any gauge-invariant physical quantities.
The gauge-invariant Green function is also studied directly in Lorentz
covariant gauge and the anomalous dimension is found to be the same as that
calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.
General form of the full electromagnetic Green function in materials physics
In this article, we present the general form of the full electromagnetic
Green function which is suitable for the application in bulk materials physics.
In particular, we show how the seven adjustable parameter functions of the free
Green function translate into seven corresponding parameter functions of the
full Green function. Furthermore, for both the fundamental response tensor and
the electromagnetic Green function, we discuss the reduction of the Dyson
equation on the four-dimensional Minkowski space to an equivalent,
three-dimensional Cartesian Dyson equation.Comment: consistent with published version in Chin. J. Phys. (2019
Thermalization of Green functions and quasinormal modes
We develop a new method to study the thermalization of time dependent
retarded Green function in conformal field theories holographically dual to
thin shell AdS Vaidya space times. The method relies on using the information
of all time derivatives of the Green function at the shell and then evolving it
for later times. The time derivatives of the Green function at the shell is
given in terms of a recursion formula. Using this method we obtain analytic
results for short time thermalization of the Green function. We show that the
late time behaviour of the Green function is determined by the first
quasinormal mode. We then implement the method numerically. As applications of
this method we study the thermalization of the retarded time dependent Green
function corresponding to a minimally coupled scalar in the AdS3 and AdS5 thin
Vaidya shells. We see that as expected the late time behaviour is determined by
the first quasinormal mode. We apply the method to study the late time
behaviour of the shear vector mode in AdS5 Vaidya shell. At small momentum the
corresponding time dependent Green function is expected to relax to equilibrium
by the shear hydrodynamic mode. Using this we obtain the universal ratio of the
shear viscosity to entropy density from a time dependent process.Comment: Typos corrected, references added, 38 pages. 9 figures. Mathematica
files included in source file
Semiclassical Green Function in Mixed Spaces
A explicit formula on semiclassical Green functions in mixed position and
momentum spaces is given, which is based on Maslov's multi-dimensional
semiclassical theory. The general formula includes both coordinate and momentum
representations of Green functions as two special cases of the form.Comment: 8 pages, typeset by Scientific Wor
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