arXiv subjects

Sebbe Stouten

Publications and source records attributed to Sebbe Stouten.

9 recordsLinked to original sources

arXiv2026

The Casimir effect in Gribov-Zwanziger theory

We consider Yang-Mills theory with two infinite parallel plates, separated by a distance \(L\), that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new \(L\)-dependencies into the GZ gap equation. This would make the Gribov mass \(\gamma\) dynamically dependent on \(L\), implying an interesting interplay with the Casimir energy. However, we show that no such dynamical \(L\)-dependence occurs within the current approximation.

hep-th↗

arXiv2026

Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory

First, we explicitly construct zero-modes of the Yang-Mills Faddeev-Popov operator in the presence of two parallel plates, with either perfect electric (PEC) or perfect magnetic (PMC) boundary conditions imposed. This establishes the existence of Gribov copies with finite action, and even finite L_2-norm, in Yang-Mills theory with non-trivial interfaces. We adapt Henyey's construction, although the boundary configuration imposes extra restrictions on the ansatz for the gauge field. Second, we discuss the phenomenon of an emergent boundary gauge invariance for PEC and PMC plates in Yang-Mills theory. This shall be important when applying the Gribov-Zwanziger procedure to parallel plate setups, of relevance for non-perturbatively studying the non-Abelian Casimir effect in the future.

hep-th↗

arXiv2026

On the Casimir effect with mixed dynamical edge mode and perfect electromagnetic conducting boundary conditions

We study the Casimir effect for a parallel plate setup with one plate with dynamical edge mode (DEM) boundary conditions, and one plate with perfect electromagnetic conductor (PEMC) boundary conditions. In order to restore BRST invariance, new edge fields are introduced on the DEM plate. We then lift the boundary conditions into the action using Lagrange multiplier fields, and integrate out the bulk fields to obtain a non-local effective boundary theory from which we compute the Casimir energy. The resulting Casimir force is identical to a PMC-PEMC setup, implying that, from the point of view of the Casimir effect, a DEM plate is equivalent to a PMC plate. We also include a detailed derivation of the general functional method used to compute the Casimir energy from the partition function.

hep-th↗

arXiv2025

Non-perturbative corrections to the Casimir energy for a scalar field theory with non-linear boundary conditions

We consider the case of a free real massive bulk scalar in D=4 dimensions, and embed two parallel plates as interfaces on which we impose non-linear boundary conditions, either Dirichlet- or Neumann-like, parameterized by a new coupling constant g. This mimics a non-Abelian gauge theory supplemented with boundary conditions on surfaces embedded in the bulk. We present the first evidence for a non-perturbative 1/g^2 boundary mass generation and its ensuing correction to the standard Casimir energy. This becomes possible by incorporating dynamical corrections to the effective boundary fields, which are used to build in the boundary conditions directly at the action level.

hep-th↗

arXiv2025

Non-Abelian Casimir energy in the Curci-Ferrari model through a functional approach

Using functional integral methods, we investigate the non-Abelian Casimir energy in the Curci-Ferrari model, which offers an effective description of the infrared regime of Yang-Mills theory. We consider a 3+1D (resp.\ 2+1D) system of two infinite parallel plates (resp.\ wires) at a fixed distance from each other, with either perfect magnetic conductor (PMC) or perfect electric conductor (PEC) boundary conditions. Imposing the boundary conditions directly in the functional integral by the introduction of suitable auxiliary fields that act as Lagrange multipliers, we obtain a boundary effective action that captures the dynamics of this system. The Casimir energy is then computed both directly from the functional integral and via the energy-momentum tensor, providing equivalent results. We find that the Casimir energy for PEC and PMC conditions differs by a constant factor, which can be traced back to a van Dam--Veltman--Zakharov-like discontinuity (both in 3+1D and 2+1D). Lastly, we show that our analytical results are compatible with a variety of recent numerical lattice simulations of the non-perturbative Yang-Mills Casimir energy, in which a novel non-perturbative mass scale emerges.

hep-th↗

arXiv2024

Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy

Recently, dynamical edge modes (DEM) in Maxwell theory have been constructed using a specific local boundary condition on the horizon. We discuss how to enforce this boundary condition on an infinite parallel plate in the QED vacuum by introducing Lagrange multiplier fields into the action. We carefully introduce appropriate boundary ghosts to maintain BRST invariance. Explicit correspondence of this BRST extended theory with the original DEM formulation is discussed, both directly, and through the correspondence between edge modes and Wilson lines attached to the boundary surface. We then use functional methods to calculate the Casimir energy for the first time with DEM boundary conditions imposed on two infinite parallel plates, both in generalized Coulomb and linear covariant gauge. Depending on the gauge, different fields are contributing, but, after correctly implementing the BRST symmetry, we retrieve the exact same Casimir energy as for two perfectly conducting parallel plates.

hep-th↗

arXiv2024

Scalar field theory under Robin boundary conditions: two-point function and energy-momentum tensor

We reconsider four-dimensional scalar field theory in presence of Robin boundary conditions on two parallel plates. These boundary conditions are directly imposed in the path integral definition of the theory via auxiliary fields living on the plates. We discuss how this leads to boundary corrections to the standard energy momentum tensor operator. Via a dimensional reduction to an effective three-dimensional boundary theory, we compute the Casimir energy in terms of the plate separation and the two Robin parameters, as well as the scalar field propagator in the presence of the plates. Coincidentally, the boundary contribution vanishes in the expectation value for the vacuum energy, thereby giving results in full accordance with other energy expressions in the literature for the same setup. We also discuss for which values of the Robin parameters this energy is real-valued.

hep-th↗

arXiv2024

A Novel Interpolation-Based Method for Solving the One-Dimensional Wave Equation on a Domain with a Moving Boundary

We revisit the problem of solving the one-dimensional wave equation on a domain with moving boundary. In J. Math. Phys. 11, 2679 (1970), Moore introduced an interesting method to do so. As only in rare cases, a closed analytical solution is possible, one must turn to perturbative expansions of Moore's method. We investigate the then made minimal assumption for convergence of the perturbation series, namely that the boundary position should be an analytic function of time. Though, we prove here that the latter requirement is not a sufficient condition for Moore's method to converge. We then introduce a novel numerical approach based on interpolation which also works for fast boundary dynamics. In comparison with other state-of-the-art numerical methods, our method offers greater speed if the wave solution needs to be evaluated at many points in time or space, whilst preserving accuracy. We discuss two variants of our method, either based on a conformal coordinate transformation or on the method of characteristics, together with interpolation.

math.NA↗

arXiv2024

The Casimir energy with perfect electromagnetic boundary conditions and duality: a field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral, and once as the vacuum expectation value of the 00-component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified, and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality-invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation.

hep-th↗