2,864 research outputs found
Light-Cone Quantization of the Liouville Model
We present the quantization of the Liouville model defined in light-cone
coordinates in (1,1) signature space. We take advantage of the representation
of the Liouville field by the free field of the Backl\"{u}nd transformation and
adapt the approch by Braaten, Curtright and Thorn.
Quantum operators of the Liouville field ,
, , are constructed consistently in
terms of the free field. The Liouville model field theory space is found to be
restricted to the sector with field momentum , , which
is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6
Lotka--Volterra Type Equations and their Explicit Integration
In the present note we give an explicit integration of some
two--dimensionalised Lotka--Volterra type equations associated with simple Lie
algebras, other than the familiar case, possessing a representation
without branching. This allows us, in particular, to treat the first
fundamental representations of , , , and on the same
footing.Comment: 3 pages LATEX fil
Scattering Mechanism in Modulation-Doped Shallow Two-Dimensional Electron Gases
We report on a systematic investigation of the dominant scattering mechanism
in shallow two-dimensional electron gases (2DEGs) formed in modulation-doped
GaAs/Al_{x}Ga_{1-x}As heterostructures. The power-law exponent of the electron
mobility versus density, mu \propto n^{alpha}, is extracted as a function of
the 2DEG's depth. When shallower than 130 nm from the surface, the power-law
exponent of the 2DEG, as well as the mobility, drops from alpha \simeq 1.65
(130 nm deep) to alpha \simeq 1.3 (60 nm deep). Our results for shallow 2DEGs
are consistent with theoretical expectations for scattering by remote dopants,
in contrast to the mobility-limiting background charged impurities of deeper
heterostructures.Comment: 4 pages, 3 figures, modified version as accepted in AP
Soliton quantization and internal symmetry
We apply the method of collective coordinate quantization to a model of
solitons in two spacetime dimensions with a global symmetry. In
particular we consider the dynamics of the charged states associated with
rotational excitations of the soliton in the internal space and their
interactions with the quanta of the background field (mesons). By solving a
system of coupled saddle-point equations we effectively sum all tree-graphs
contributing to the one-point Green's function of the meson field in the
background of a rotating soliton. We find that the resulting one-point function
evaluated between soliton states of definite charge exhibits a pole on
the meson mass shell and we extract the corresponding S-matrix element for the
decay of an excited state via the emission of a single meson using the standard
LSZ reduction formula. This S-matrix element has a natural interpretation in
terms of an effective Lagrangian for the charged soliton states with an
explicit Yukawa coupling to the meson field. We calculate the leading-order
semi-classical decay width of the excited soliton states discuss the
consequences of these results for the hadronic decay of the resonance
in the Skyrme model.Comment: 23 pages, LA-UR-93-299
Correlation functions in super Liouville theory
We calculate three- and four-point functions in super Liouville theory
coupled to super Coulomb gas on world sheets with spherical topology. We first
integrate over the zero mode and assume that a parameter takes an integer
value. After calculating the amplitudes, we formally continue the parameter to
an arbitrary real number. Remarkably the result is completely parallel to the
bosonic case, the amplitudes being of the same form as those of the bosonic
case.Comment: 11 page
Photon Production from a Quark-Gluon-Plasma at Finite Baryon Chemical Potential
We compute the photon production of a QCD plasma at leading order in the
strong coupling with a finite baryon chemical potential. Our approach starts
from the real time formalism of finite temperature field theory. We identify
the class of diagrams contributing at leading order when a finite chemical
potential is added and resum them to perform a full treatment of the LPM effect
similar to the one performed by Arnold, Moore, and Yaffe at zero chemical
potential. Our results show that the contribution of and processes grows as the chemical potential grows.Comment: 28 pages, 14 figure
Free fields via canonical transformations of matter-coupled 2D dilaton gravity models
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late
Multi-Component KdV Hierarchy, V-Algebra and Non-Abelian Toda Theory
I prove the recently conjectured relation between the -matrix
differential operator , and a certain non-linear and non-local
Poisson bracket algebra (-algebra), containing a Virasoro subalgebra, which
appeared in the study of a non-abelian Toda field theory. Here, I show that
this -algebra is precisely given by the second Gelfand-Dikii bracket
associated with . The Miura transformation is given which relates the second
to the first Gelfand-Dikii bracket. The two Gelfand-Dikii brackets are also
obtained from the associated (integro-) differential equation satisfied by
fermion bilinears. The asymptotic expansion of the resolvent of
is studied and its coefficients yield an infinite sequence of
hamiltonians with mutually vanishing Poisson brackets. I recall how this leads
to a matrix KdV hierarchy which are flow equations for the three component
fields of . For they reduce to the ordinary KdV
hierarchy. The corresponding matrix mKdV equations are also given, as well as
the relation to the pseudo- differential operator approach. Most of the results
continue to hold if is a hermitian -matrix. Conjectures are made
about -matrix -order differential operators and
associated -algebras.Comment: 20 pages, revised: several references to earlier papers on
multi-component KdV equations are adde
Quantum Hamilton-Jacobi equation
The nontrivial transformation of the phase space path integral measure under
certain discretized analogues of canonical transformations is computed. This
Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation
for the generating function of a canonical transformation that maps any quantum
system to a system with a vanishing Hamiltonian. A formal perturbative solution
of the quantum Hamilton-Jacobi equation is given.Comment: 4 pages, RevTe
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