Quantum effects due to a moving Dirichlet point

Abstract

We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field ϕ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong coupling limit of a term quadratic in the field and localized on the particle's trajectory. We discuss the renormalization issues that appear and evaluate the effective action. Special attention is paid to the case of 2 spatial dimensions where the coupling constant is adimensional. arXiv:1910.12737v1 [hep-th] 28 Oct 2019 quanta when a field is subjected to time-dependent boundary conditions, an example being the presence of one or more moving mirrors, namely, of objects imposing non-trivial boundary conditions on the field. In the usual understanding of the term, a boundary condition acts on a region having co-dimension one, i.e., which is determined by a single equation. It is worth noting that, in the context of the DCE for a real scalar field, which we consider here, different kinds of boundary conditions, besides the 'perfect' ones (Dirichlet and Neumann), have also been studied. Those 'imperfect' conditions describe mirrors which have more realistic responses to the action of the field's modes. Among that kind of condition, a relatively simple one amounts to Dirichlet-like boundary conditions: they result from the addition to the action of a term localized on the space-time region which is swept by the mirror during the course of time. When the strength of that term tends to infinity, one gets Dirichlet conditions on the region on which the term is localized. It is our concern in this paper to study the DCE, for the case of a real scalar field ϕ in d + 1 dimensions (d = 1, 2, 3), coupled to point-like objects which implement precisely that kind of Dirichlet-like boundary conditions. In other words, we shall add to the scalar field Lagrangian a term proportional to a δ-function of the (time-dependent) position of the particle, and to the square of ϕ. The strength of the term is determined by a coupling constant which, by taking the appropriate limit, will be used to impose Dirichlet boundary conditions. We shall follow our previous work for scalar and spinorial vacuum fields [4,5] in which we used the particularly convenient functional approach proposed by Golestanian and Kardar [6]. The approach is based on the use of auxiliary fields to deal with the role of the mirrors, on the calculation of the functional integral for the in-out effective action. An important feature of the systems that we consider here is the following: except for d = 1 a curve, like the particle's world-line, has codimension bigger than 1; this fact results in qualitatively different UV properties during the calculation of the effective action. Indeed, the UV problems which will arise here are rather similar to the ones corresponding to Dirac δ-potentials in 2 and 3 dimensions, a system which has been extensively studied by following many different approaches and frameworks (see, for example, [7,8,9,10]). Note t...

Vacuum Radiation from Massive Scalar Field

“…In this paper, we study the emission of particles from a massive scalar field vacuum with a single moving perfect reflective mirror. As an extension of the results obtained for the same physical system [21,22], we obtain the vacuum friction force and the spatial spectra of the emitted particles. Despite the generality and efficiency of the path integral method [21,22,24], we use the canonical quantization method, together with the scattering theory formula, because they can be used to express the vacuum radiation process more clearly, with the pair emission of vacuum radiation demonstrated by means of the negative sea picture [13].…”

“…The vacuum friction effect and motion fluctuation of a mirror with an internal degree of freedom on a specified worldline is given in [20]. The vacuum radiation power, as well as the Euclidean effective action, of massive field coupled to a moving mirror are derived by means of the path integral approach in [21,22]. Furthermore, the dynamical Casimir effect of a massive field in the presence of two mirrors is considered in [23,24].…”

Study of Gribov Copies in the Yang-Mills ensemble

“…In ref. [36], the dynamical Casimir effect associated to a moving Dirichlet point was discussed for d = 1, 2, 3. The case d ≥ 2 was found more subtle to deal with, as it is necessary to renormalize the coupling to obtain a finite effective action for the particle.…”

Vacuum radiation from massive scalar field

“…This suggests it is natural to generalize the methods used in studying dynamical Casimir effect of massless field to that of massive field [19]. Actually, there are many results of massive theories obtained by different approaches in various situations [20,21,22,23,24].…”

“…In this paper, we study the emission of massive particles from vacuum with single moving perfect reflective mirror and the vacuum friction force on the mirror. Despite the generality and efficiency of the path integral method [22,23,24], we use canonical quantization method together with the scattering theory formula because they pictures the vacuum radiation process clearer. The pair emission nature of vacuum radiation can be intuitionally demonstrated by the negative sea picture originally introduced in [19].…”