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

Global phase time and path integral for string cosmological models

A global phase time is identified for homogeneous and isotropic cosmological models yielding from the low energy effective action of closed bosonic string theory. When the Hamiltonian constraint allows for the existence of an intrinsic time, the quantum transition amplitude is obtained by means of the usual path integral procedure for gauge systems.Comment: 12 pages, added reference

Gauge invariance of parametrized systems and path integral quantization

Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called ``ideal clock'', and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.Comment: 23 page

Global phase time and path integral for the Kantowski--Sachs anisotropic univers

The action functional of the anisotropic Kantowski--Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum transition amplitude is obtained by means of the usual path integral procedure of Fadeev and Popov.Comment: 11 page

Radiation reaction for multipole moments

We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.Comment: 12 pages, 1 figure, RevTeX 4; references updated, minor textual correction

Long time black hole evaporation with bounded Hawking flux

The long time behavior of an evaporating Schwarzschild black hole is studied exploiting that it can be described by an effective theory in 2D, a particular dilaton gravity model. A crucial technical ingredient is Izawa's result on consistent deformations of 2D BF theory, while the most relevant physical assumption is boundedness of the asymptotic matter flux during the whole evaporation process. An attractor solution, the endpoint of the evaporation process, is found. Its metric is flat. However, the behavior of the dilaton field is nontrivial: it is argued that during the final flicker a first order phase transition occurs from a linear to a constant dilaton vacuum, thereby emitting a shock wave with a total energy of a fraction of the Planck mass. Another fraction of the Planck mass may reside in a cold remnant. [Note: More detailed abstract in the paper]Comment: 34 pages, 6 figures, v2: included new references and 2 new footnotes; v3: mayor revisions (extended intro, included pedagogical example, rearranged presentation, extended discussion on information paradox, updated references); v4: updated refs. (+ new ones), added comments, mostly on dilaton evaporation, rewrote abstract (short for arXiv, long for journal), moved pedagogic sec. to ap