We study, using Rindler coordinates, the quantization of a charged scalar field interacting with a constant (Poincaré invariant), external, electric field in (1+1) dimensionnal flatspace: our main motivation is pedagogy. We illustrate in this framework the equivalence between various approaches to field quantization commonly used in the framework of curved backgrounds. First we establish the expression of the Schwinger vacuum decay rate, using the operator formalism. Then we rederive it in the framework of the Feynman path integral method. Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propagator. Moreover we compute the expression of the Unruh's modes that allow to make connection between Minkowskian and Rindlerian quantization scheme by purely algebraic relations. We use these modes to study the physics of a charged two level detector moving in an electric field whose transitions are due to the exchange of charged quanta. In the limit where the Schwinger pair production mechanism of the exchanged quanta becomes negligible we recover the Boltzman equilibrium ratio for the population of the levels of the detector. Finally we explicitly show how the detector can be taken as the large mass and charge limit of an interacting fields system.

We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one). We show that the construction of the maximally localized states based on squeezed states generally fails. Rather, one must resort to a constrained variational principle.Comment: accepted for publication in PR

The minimal length uncertainty principle of Kemf, Mangano and Mann ͑KMM͒, as derived from a mutilated quantum commutator between coordinate and momentum, is applied to describe the modes and wave packets of Hawking particles evaporated from a black hole. The trans-Planckian problem is successfully confronted in that the Hawking particle no longer hugs the horizon at arbitrarily close distances. Rather the mode of Schwarzschild frequency deviates from the conventional trajectory when the coordinate r is given by ͉rϪ2M ͉Ӎ␤ H /2 in units of the nonlocal distance legislated into the uncertainty relation. Wave packets straddle the horizon and spread out to fill the whole nonlocal region. The charge carried by the packet ͑in the sense of the amount of ''stuff'' carried by the Klein-Gordon field͒ is not conserved in the non-local region and rapidly decreases to zero as time decreases. Read in the forward temporal direction, the non-local region thus is the seat of production of the Hawking particle and its partner. The KMM model was inspired by string theory for which the mutilated commutator has been proposed to describe an effective theory of high momentum scattering of zero mass modes. It is here interpreted in terms of dissipation which gives rise to the Hawking particle into a reservoir of other modes ͑of as yet unknown origin͒. On this basis it is conjectured that the Bekenstein-Hawking entropy finds its origin in the fluctuations of fields extending over the nonlocal region.

We compute the Pauli-Jordan, Hadamard and Feynman propagators for the massive metrical perturbations on de Sitter space. They are expressed both in terms of mode sums and in invariant forms.

In this paper, we study by a functional method the vacuum instability of a charged scalar field, when it is quantized in the background of the ReissnerNordström black hole; we also show that the first stage of the evaporation process of the black hole can be driven by a Schwinger-like effect.