18,871 research outputs found
The asymptotic behaviour of the exact and approximative Chern-Simons Green's functions
We consider the asymptotic behaviour of the Chern-Simons Green's function of
the system for an infinite area in position-time
representation. We calculate explicitly the asymptotic form of the Green's
function of the interaction free Chern-Simons system for small times. The
calculated Green's function vanishes exponentially with the logarithm of the
area. Furthermore, we discuss the form of the divergence for all and
also for the Coulomb interacting Chern-Simons system. We compare the
asymptotics of the exact Chern-Simons Green's function with the asymptotics of
the Green's function in the Hartree-Fock as well as the random-phase
approximation (RPA). The asymptotics of Hartree-Fock the Green's function
corresponds well with the exact Green's function. In the case of the RPA
Green's function we do not get the correct asymptotics. At last, we calculate
the self consistent Hartree-Fock Green's function.Comment: 12 Revtex pages, 1 eps figure, using style files pst-feyn.sty,
pst-key.sty, typos correcte
Universal behavior of quantum Green's functions
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined
in a d-dimensional domain. The object of interest is the time-independent Green
function G_z(r,r') = . Recently, in one dimension (1D),
the Green's function problem was solved explicitly in inverse form, with
diagonal elements of Green's function as prescribed variables. The first aim of
this paper is to extract from the 1D inverse solution such information about
Green's function which cannot be deduced directly from its definition. Among
others, this information involves universal, i.e. u(r)-independent, behavior of
Green's function close to the domain boundary. The second aim is to extend the
inverse formalism to higher dimensions, especially to 3D, and to derive the
universal form of Green's function for various shapes of the confining domain
boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy
Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
We propose several topological order parameters expressed in terms of Green's
function at zero frequency for topological superconductors, which generalizes
the previous work for interacting insulators. The coefficient in topological
field theory is expressed in terms of zero frequency Green's function. We also
study topological phase transition beyond noninteracting limit in this zero
frequency Green's function approach.Comment: 10 pages. Published versio
Green's function for gravitational waves in FRW spacetimes
A method for calculating the retarded Green's function for the gravitational
wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of
linearized Einstein gravity is developed. Hadamard's general solution to
Cauchy's problem for second-order, linear partial differential equations is
applied to the FRW gravitational wave equation. The retarded Green's function
may be calculated for any FRW spacetime, with curved or flat spatial sections,
for which the functional form of the Ricci scalar curvature is known. The
retarded Green's function for gravitational waves propagating through a
cosmological fluid composed of both radiation and dust is calculated
analytically for the first time. It is also shown that for all FRW spacetimes
in which the Ricci scalar curvatures does not vanish, , the Green's
function violates Huygens' principle; the Green's function has support inside
the light-cone due to the scatter of gravitational waves off the background
curvature.Comment: 9 pages, FERMILAB-Pub-93/189-
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