7 research outputs found
Performance statistics of the FORTRAN 4 /H/ library for the IBM system/360
Test procedures and results for accuracy and timing tests of the basic IBM 360/50 FORTRAN 4 /H/ subroutine library are reported. The testing was undertaken to verify performance capability and as a prelude to providing some replacement routines of improved performance
Modular localization and Wigner particles
We propose a framework for the free field construction of algebras of local
observables which uses as an input the Bisognano-Wichmann relations and a
representation of the Poincare' group on the one-particle Hilbert space. The
abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us
to bypass some limitations of the Wigner formalism by introducing an intrinsic
spacetime localization. Our approach works also for continuous spin
representations to which we associate a net of von Neumann algebras on
spacelike cones with the Reeh-Schlieder property. The positivity of the energy
in the representation turns out to be equivalent to the isotony of the net, in
the spirit of Borchers theorem. Our procedure extends to other spacetimes
homogeneous under a group of geometric transformations as in the case of
conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev.
Math. Phy
Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions
The potential group method is applied to the n-dimensional
Coulomb-Rosochatius potential, whose bound states and scattering states are
worked out in detail. As far as scattering is concerned, the S-matrix elements
are computed by the method of intertwining operators and an integral
representation is obtained for the scattering amplitude. It is shown that the
maximal superintegrability of the system is due to the underlying potential
group and that the 2n-1 constants of motion are related to Casimir operators of
subgroups.Comment: 14 pages, 1 figure, to appear in J. Phys. A : Math. Theo
Group theoretical approach to quantum fields in de Sitter space I. The principal series
Using unitary irreducible representations of the de Sitter group, we
construct the Fock space of a massive free scalar field.
In this approach, the vacuum is the unique dS invariant state. The quantum
field is a posteriori defined by an operator subject to covariant
transformations under the dS isometry group. This insures that it obeys
canonical commutation relations, up to an overall factor which should not
vanish as it fixes the value of hbar. However, contrary to what is obtained for
the Poincare group, the covariance condition leaves an arbitrariness in the
definition of the field. This arbitrariness allows to recover the amplitudes
governing spontaneous pair creation processes, as well as the class of alpha
vacua obtained in the usual field theoretical approach. The two approaches can
be formally related by introducing a squeezing operator which acts on the state
in the field theoretical description and on the operator in the present
treatment. The choice of the different dS invariant schemes (different alpha
vacua) is here posed in very simple terms: it is related to a first order
differential equation which is singular on the horizon and whose general
solution is therefore characterized by the amplitude on either side of the
horizon. Our algebraic approach offers a new method to define quantum field
theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc
On the cubic interactions of massive and partially-massless higher spins in (A)dS
Cubic interactions of massive and partially-massless totally-symmetric
higher-spin fields in any constant-curvature background of dimension greater
than three are investigated. Making use of the ambient-space formalism, the
consistency condition for the traceless and transverse parts of the
parity-invariant interactions is recast into a system of partial differential
equations. The latter can be explicitly solved for given s_1-s_2-s_3 couplings
and the 2-2-2 and 3-3-2 examples are provided in detail for general choices of
the masses. On the other hand, the general solutions for the interactions
involving massive and massless fields are expressed in a compact form as
generating functions of all the consistent couplings. The St\"uckelberg
formulation of the cubic interactions as well as their massless limits are also
analyzed.Comment: 42 pages, 2 tables, LaTex. Comments on two-derivative couplings
involving partially-massless spin-2 fields added, typos corrected, references
added. v2: final version to appear in JHEP. v3: formulae (3.4) and (3.9)
correcte