5 research outputs found
Principal models on a solvable group with nonconstant metric
Field equations for generalized principle models with nonconstant metric are
derived and ansatz for their Lax pairs is given. Equations that define the Lax
pairs are solved for the simplest solvable group. The solution is dependent on
one free variable that can serve as the spectral parameter. Painleve analysis
of the resulting model is performed and its particular solutions are foundComment: 8 pages, Latex2e, no figure
Time evolution and observables in constrained systems
The discussion is limited to first-class parametrized systems, where the
definition of time evolution and observables is not trivial, and to finite
dimensional systems in order that technicalities do not obscure the conceptual
framework. The existence of reasonable true, or physical, degrees of freedom is
rigorously defined and called {\em local reducibility}. A proof is given that
any locally reducible system admits a complete set of perennials. For locally
reducible systems, the most general construction of time evolution in the
Schroedinger and Heisenberg form that uses only geometry of the phase space is
described. The time shifts are not required to be 1symmetries. A relation
between perennials and observables of the Schroedinger or Heisenberg type
results: such observables can be identified with certain classes of perennials
and the structure of the classes depends on the time evolution. The time
evolution between two non-global transversal surfaces is studied. The problem
is posed and solved within the framework of the ordinary quantum mechanics. The
resulting non-unitarity is different from that known in the field theory
(Hawking effect): state norms need not be preserved so that the system can be
lost during the evolution of this kind.Comment: 31 pages, Latex fil
Geometry and Integrability of Topological-Antitopological Fusion
Integrability of equations of topological-antitopological fusion (being
proposed by Cecotti and Vafa) describing ground state metric on given 2D
topological field theory (TFT) model, is proved. For massive TFT models these
equations are reduced to a universal form (being independent on the given TFT
model) by gauge transformations. For massive perturbations of topological
conformal field theory models the separatrix solutions of the equations bounded
at infinity are found by the isomonodromy deformations method. Also it is shown
that ground state metric together with some part of the underlined TFT
structure can be parametrized by pluriharmonic maps of the coupling space to
the symmetric space of real positive definite quadratic forms.Comment: 30 pages, plain TEX, INFN-8/92-DS