Vacuum polarization of a massive scalar field in the background of a two-dimensional version of a spinning cosmic string is investigated. It is shown that when the "radius of the universe" is such that spacetime is globally hyperbolic the vacuum fluctuations are well behaved, diverging though on the "chronology horizon". Naive use of the formulas when spacetime is nonglobally hyperbolic leads to unphysical results. It is also pointed out that the set of normal modes used previously in the literature to address the problem gives rise to two-point functions which do not have a Hadamard form, and therefore are not physically acceptable. Such normal modes correspond to a locally (but not globally) Minkowski time, which appears to be at first sight a natural choice of time to implement quantization.PACS numbers: 04.70. Dy, 04.62.+v The study of quantum fields around cosmic strings is a pertinent issue since such defects may play a role in the cosmological scenario [1]. Most of the literature concerns spinless cosmic strings (see Ref.[1] and references therein), and only a few works have considered quantum mechanics and quantum field theory around spinning cosmic strings [2,3,4,5,6,7].The locally flat spacetime around an infinitely thin spinning cosmic string [1] is characterized by the line elementand by the identification (τ, ρ, ϕ, z) ∼ (τ, ρ, ϕ + 2π, z), where 0 < α ≤ 1 is the cone parameter and S ≥ 0 is the spin density (clearly the Minkowski spacetime corresponds to S = 0 and α = 1). As the region for which ρ < S/α contains closed timelike contours the spacetime is not globally hyperbolic. In other words a global time is not available, so that it is not clear whether quantum theory makes sense in this background [8].The study of a relativistic quantum scalar particle moving on the spinning cone [the corresponding threedimensional line element is obtained from Eq. (1) by setting dz = 0] has shown that a nonvanishing S spoils unitarity [2]. It has been speculated that this sort of first quantized pathology could be eliminated in the second quantized approach. However, Ref. [7] seems to frustrate this possibility by showing that the vacuum fluctuations of a massless scalar field diverge on concentric cylindrical shells around the spinning cosmic string. These pathological results have been attributed to the nonglobally hyperbolic nature of the background.In order to exhibit clearly aspects of global hyperbolicity (and related issues) in actual calculations, this work will consider a toy model which consists of a quantum scalar field existing in a two dimensional spacetime whose line element is obtained by truncating Eq. (1) as [5](α was dropped since it can be removed by redefining the parameter ρ) and observingIt is clear that S = 0 corresponds to a cylindrical spacetime of periodicity length 2πρ. The main pedagogical feature of this toy model is that, for a given "radius of the universe" ρ > 0, one can tune the spin S such that the background is globally hyperbolic (ρ > S) or otherwise (ρ ≤ S). Assuming ρ > S a...

Representations of the Klein-Gordon and Dirac propagators are determined in a $N$ dimensional conical background for massive fields twisted by an arbitrary angle $2\pi\sigma$. The Dirac propagator is shown to be obtained from the Klein-Gordon propagator twisted by angles $2\pi\sigma\pm {\cal D}/2$ where ${\cal D}$ is the cone deficit angle. Vacuum expectation values are determined by a point-splitting method in the proper time representation of the propagators. Analogies with the Aharonov-Bohm effect are pointed out throughout the paper and a conjecture on an extension to fields of arbitrary spin is given.Comment: Propagator (11) is rewritten in a more convenient form and the one before that is amended. A more concise expression is given for the energy density of a twisted spinor. The references contain minor correction

The renormalized Feynman propagator for a scalar field in the background of a cosmic dispiration (a disclination plus a screw dislocation) is derived, opening a window to investigate vacuum polarization effects around a cosmic string with dislocation, as well as in the bulk of an elastic solid carrying a dispiration. The use of the propagator is illustrated by computing vacuum fluctuations. In particular it is shown that the dispiration polarizes the vacuum giving rise to an energy momentum tensor which, as seen from a local inertial frame, presents non vanishing off-diagonal components. Such a new effect resembles that where an induced vacuum current arises around a needle solenoid carrying a magnetic flux (the Aharonov-Bohm effect), and may have physical consequences. Connections with a closely related background, namely the spacetime of a spinning cosmic string, are briefly addressed.

The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity and position of the particle are explicitly derived and their behaviors examined. The results are similar to those corresponding to an electric charge interacting with a quantum electromagnetic field near a reflecting plane boundary, mainly regarding the divergent behavior of the dispersions at the origin (where the boundary is placed), and at the time interval corresponding to a round trip of a light pulse between the particle and the boundary.We close by addressing some effects of allowing the position of the particle to fluctuate.

This paper investigates the thermodynamics of a large class of non-Hermitian, P T -symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very accurate even for small quantum numbers, and used to generate the quantum partition function. Graphs showing the thermal behavior of the entropy and the specific heat, at all regimes of temperature, are given. To obtain the corresponding classical partition function it turns out to be necessary in general to integrate over a complex "phase space". For the wrong-sign quartic, whose equivalent Hermitian Hamiltonian is known exactly, it is demonstrated explicitly how this formulation arises, starting from the Hermitian case.