/ 99 07 05 5 v 1 8 J ul 1 99 9 IPM / P - 99 / 037 hep - th / 9907055 Boundary Conditions as Dirac Constraints

X iv : h ep - t h / 99 07 05 5 v 2 1 0 Ju l 1 99 9 IPM / P - 99 / 037 hep - th / 9907055 Boundary Conditions as Dirac Constraints

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

ar X iv : h ep - t h / 92 06 05 6 v 2 8 J ul 1 99 3 hep - th / 9206056 UCSBTH – 92 – 22 Revised July 1993 IS PURITY ETERNAL ?

Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.

ar X iv : g r - qc / 9 80 70 11 v 1 6 J ul 1 99 8 Constraints on spacetime manifold in Euclidean supergravity in terms of Dirac eigenvalues

We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold, under which spacetime addmits Dirac eigenvalues as observables, are derived. Typeset using REVTEX

ar X iv : h ep - t h / 99 07 14 9 v 1 1 7 Ju l 1 99 9 Non linear σ models : renormalisability versus geometry . ∗

After some recalls on the standard (non)-linear σ model, we discuss the interest of B.R.S. symmetry in non-linear σ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical constraints rather than as given by a particular Lagrangian and discuss some ways to enlarge the notion of renormalisability. PAR/LPTHE/99-27/hep-th/xxx July 99 Talk given...

ar X iv : h ep - p h / 97 05 45 5 v 1 2 8 M ay 1 99 7 LECTURE 1 Spectral Fluctuations of the QCD Dirac Operator