arXiv subjects

E. Huguet

Publications and source records attributed to E. Huguet.

27 records · Page 2Linked to original sources

arXiv2010

Conformally covariant quantization of Maxwell field in de Sitter space

In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de Sitter invariant two-points function which is very simple. Our method relies on the one hand on a geometrical point of view which uses the realization of Minkowski, de Sitter and anti-de Sitter spaces as intersections of the null cone in $\setR^6$ and a moving plane, and on the other hand on a canonical quantization scheme of the Gupta-Bleuler type.

gr-qc↗

arXiv2008

Revisiting the conformal invariance of the scalar field: from Minkowski space to de Sitter space

In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (i.e. SO(2,$d$)) invariance of the conformal scalar field on both spaces. We exhibit the realization on de Sitter space of the massless scalar representation of SO$(2,d)$. It is obtained from the corresponding representation in Minkowski space through an intertwining operator inherited from the Weyl relation between the two spaces. The de Sitter representation is written in a form which allows one to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms.

gr-qc↗

arXiv2007

Wick ordering for coherent state quantization in 1+1 de Sitter space

We show that the coherent state quantization of massive particles in 1+1 de Sitter space exhibits an ordering property: There exist some classical observables $A$ and $A^*$ such that $O_{A^{*p}}O_{A^q}=O_{A^{*p} A^q}$ $p, q \in \Z$, where $O_A$ is the quantum observable corresponding to the classical observable $A$.

math-ph↗

arXiv2006

A toy model of a fake inflation

Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on Electrodynamics in the cosmic geometry. Such phenomenon of induced metric is rather general and may occurs for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of non linear scalar field. We show that a class of theories that have been analyzed in the literature, having regular configuration in the Minkowski space-time background is such that the field propagates like free waves in an effective deSitter geometry. The observation of these waves would led us to infer, erroneously, that we live in a deSitter universe.

astro-ph↗

arXiv2006

Conformally related massless fields in dS, AdS and Minkowski spaces

In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski spacetime in d-dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and two-points functions, turns to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.

gr-qc↗

arXiv2004

Krein space quantization in curved and flat spacetimes

We reexamine in detail a canonical quantization method a la Gupta-Bleuler in which the Fock space is built over a so-called Krein space. This method has already been successfully applied to the massless minimally coupled scalar field in de Sitter spacetime for which it preserves covariance. Here, it is formulated in a more general context. An interesting feature of the theory is that, although the field is obtained by canonical quantization, it is independent of Bogoliubov transformations. Moreover no infinite term appears in the computation of $T^{μν}$ mean values and the vacuum energy of the free field vanishes: $<0|T^{00}|0>=0$. We also investigate the behaviour of the Krein quantization in Minkowski space for a theory with interaction. We show that one can recover the usual theory with the exception that the vacuum energy of the free theory is zero.

gr-qc↗

arXiv2003

De Sitter Waves and the Zero Curvature Limit

We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far as one wishes to recover ordinary QFT in the flat limit.

gr-qc↗

arXiv2003

Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval

We present a quantization scheme of an arbitrary measure space based on overcomplete families of states and generalizing the Klauder and the Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods like geometric quantization are uneasy to implement. The procedure is illustrated by (mostly two-dimensional) elementary examples in which the measure space is a $N$-element set and the unit interval. Spaces of states for the $N$-element set and the unit interval are the 2-dimensional euclidean $\R^2$ and hermitian $\C^2$ planes.

quant-ph↗

arXiv1999

Bound states in monopoles: sources for UHECR ?

Bound states in monopoles are studied through a simplified, Witten-like model. As the overall structure is determined in full details, it is shown in particular that only those states having a vanishing angular momentum are allowed; for those, the energy spectrum is derived numerically and an approximation is set up that allows an easy description in terms of wavefunctions, usefull for further applications. The monopoles are then proposed as candidates of ultra high energy cosmic rays, an hypothesis that should soon be testable through the Pierre Auger Observatory.

hep-ph↗