188 research outputs found
Conservation laws for the classical Toda field theories
We have performed some explicit calculations of the conservation laws for
classical (affine) Toda field theories, and some generalizations of these
models. We show that there is a huge class of generalized models which have an
infinite set of conservation laws, with their integrated charges being in
involution. Amongst these models we find that only the and
() Toda field theories admit such conservation laws for spin-3. We
report on our explicit calculations of spin-4 and spin-5 conservation laws in
the (affine) Toda models. Our perhaps most interesting finding is that there
exist conservation laws in the models ( which have a different
origin than the exponents of the corresponding affine theory or the
energy-momentum tensor of a conformal theory.Comment: 9 pages, Late
Using Conservation Laws to Solve Toda Field Theories
We investigate the question of how the knowledge of sufficiently many local
conservation laws for a model can be utilized to solve the model. We show that
for models where the conservation laws can be written in one-sided forms, like
\barpartial Q_s = 0, the problem can always be reduced to solving a closed
system of ordinary differential equations. We investigate the , , and
Toda field theories in considerable detail from this viewpoint. One of
our findings is that there is in each case a transformation group intrinsic to
the model. This group is built on a specific real form of the Lie algebra used
to label the Toda field theory. It is the group of field transformations which
leaves the conserved densities invariant.Comment: Latex, 24 page
On the form of local conservation laws for some relativistic field theories in 1+1 dimensions
We investigate the possible form of local translation invariant conservation
laws associated with the relativistic field equations
\partial\bar\partial\phi_i=-v_i(\bphi) for a multicomponent field \bphi.
Under the assumptions that (i)~the 's can be expressed as linear
combinations of partial derivatives of a set of
functions w_j(\bphi), (ii)~the space of functions spanned by the 's is
closed under partial derivations, and (iii)~the fields \bphi take values in a
simply connected space, the local conservation laws can either be transformed
to the form (where
and are homogeneous polynomials in the variables
, ,\ldots), or to the parity
transformed version of this expression .Comment: 12 pages, Late
Problem Areas Concerning Foreign Investment in U.S. Real Estate
Current problems related to foreign investment in real estate have a long and involved history. After a brief historical review, this per- spective will consider present limitations on alien ownership of real es- tate, inconveniences such as disclosure of ownership, and incidental administrative side effects which place the foreign investor in a differ- ent position than a U.S. investor
Problem Areas Concerning Foreign Investment in U.S. Real Estate
Current problems related to foreign investment in real estate have a long and involved history. After a brief historical review, this per- spective will consider present limitations on alien ownership of real es- tate, inconveniences such as disclosure of ownership, and incidental administrative side effects which place the foreign investor in a differ- ent position than a U.S. investor
Electromagnetic Casimir energy with extra dimensions
We calculate the energy-momentum tensor due to electromagnetic vacuum
fluctuations between two parallel hyperplanes in more than four dimensions,
considering both metallic and MIT boundary conditions. Using the axial gauge,
the problem can be mapped upon the corresponding problem with a massless,
scalar field satisfying respectively Dirichlet or Neumann boundary conditions.
The pressure between the plates is constant while the energy density is found
to diverge at the boundaries when there are extra dimensions. This can be
related to the fact that Maxwell theory is then no longer conformally
invariant. A similar behavior is known for the scalar field where a constant
energy density consistent with the pressure can be obtained by improving the
energy-momentum tensor with the Huggins term. This is not possible for the
Maxwell field. However, the change in the energy-momentum tensor with distance
between boundaries is finite in all cases.Comment: 16 pages, typos corrected, published versio
Equation of State for Exclusion Statistics in a Harmonic Well
We consider the equations of state for systems of particles with exclusion
statistics in a harmonic well. Paradygmatic examples are noninteracting
particles obeying ideal fractional exclusion statistics placed in (i) a
harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level
(LLL) of an exterior magnetic field. We show their identity with (i) the
Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in
a harmonic well.Comment: latex file, 11 page
ON THERMODYNAMICS OF MULTISPECIES ANYONS
We address the problem of multispecies anyons, i.e. particles of different
species whose wave function is subject to anyonlike conditions. The cluster and
virial coefficients are considered. Special attention is paid to the case of
anyons in the lowest Landau level of a strong magnetic field, when it is
possible (i) to prove microscopically the equation of state,
in particular in terms of Aharonov-Bohm charge-flux composite systems, and
(ii) to formulate the problem in terms of single-state statistical
distributions.Comment: Latex, 19 page
Non-Abelian Chern-Simons Particles in an External Magnetic Field
The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons
particles (non-Abelian anyons) in an external magnetic field are addressed. We
derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the Hilbert
space is projected onto the lowest Landau level of the magnetic field. In the
presence of an additional harmonic potential, the N-body spectrum depends
linearly on the coupling (statistics) parameter. We calculate the second virial
coefficient and find that in the strong magnetic field limit it develops a
step-wise behavior as a function of the statistics parameter, in contrast to
the linear dependence in the case of Abelian anyons. For small enough values of
the statistics parameter we relate the N-body partition functions in the lowest
Landau level to those of SU(2) bosons and find that the cluster (and virial)
coefficients dependence on the statistics parameter cancels.Comment: 35 pages, revtex, 3 eps figures include
Radiative Corrections to the Casimir Energy
The lowest radiative correction to the Casimir energy density between two
parallel plates is calculated using effective field theory. Since the
correlators of the electromagnetic field diverge near the plates, the
regularized energy density is also divergent. However, the regularized integral
of the energy density is finite and varies with the plate separation L as
1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but
more transparent theory of a massless scalar field in 1+1 dimensions confined
to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late
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