Energy-Momentum Tensors With Worldline Numerics

Schäfer, Marco; Huet, Idrish; Gies, Holger

doi:10.1142/s2010194512007647

Cited by 6 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this context, worldline based numerical analysis has been used to determine the range of validity of the scheme known as proximity force approximation [35,36]. In [37,38] the method was tested by computing the positive-energy conditions in various Casimir settings. These numerical methods are based on a Monte Carlo generation of worldline ensembles which, apart from providing an intuitive picture of the nonlocal nature of quantum fluctuations, is comparatively cheap due to its probabilistic nature (see [39,40,41,42]); we consider our analytic expressions could be used to test numerical computations in spherical geometries.…”

Section: Discussionmentioning

confidence: 99%

Worldline formalism for a confined scalar field

Corradini

Edwards

Huet

et al. 2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field which is confined within some boundaries one needs to restrict the path integration domain of the auxiliary point-particle to a specific subset of worldlines enclosed by those boundaries. We show how to implement this restriction for the case of a scalar field confined to the D-dimensional ball under Dirichlet and Neumann boundary conditions, and compute the first few heat-kernel coefficients as a verification of our construction. We argue that this approach could admit different generalizations.

show abstract

Section: Discussionmentioning

confidence: 99%

Worldline formalism for a confined scalar field

Corradini

Edwards

Huet

et al. 2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This v lines algorithm is a generalization of the efficient v loops algorithm introduced in [48] which generates corresponding closed worldlines. Open worldlines can also efficiently be generated by a variant of the d loop algorithm [18] that also works for open lines [58,59], however, the following v lines algorithm can be employed for an arbitrary number of points (for d lines or loops they always come in powers of 2).…”

Section: Discussionmentioning

confidence: 99%

Propagator from nonperturbative worldline dynamics

Franchino-Viñas

Gies

2019

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling in the quenched limit (small-N f expansion). Specifically, we consider a simple two-scalar field theory with cubic interaction (S 2 QED) in four dimensions as a toy model for QED-like theories. Using a worldline regularization technique, we are able to analyze the divergence structure of all-order diagrams and to perform the renormalization of the model nonperturbatively. Our method gives us access to a wide range of couplings and coordinate distances. We compute the pole mass of the S 2 QED electron and observe sizable nonperturbative effects in the strong-coupling regime arising from the full photon dressing. We also find indications for the existence of a critical coupling where the photon dressing compensates the bare mass such that the electron mass vanishes. The short distance behavior remains unaffected by the photon dressing in accordance with the power-counting structure of the model.

show abstract

“…(24) and (25) can yield CasimirPolder energies for an atom interacting with a macroscopic body by treating the atom as a small chunk of magnetodielectric material. However, this is numerically inefficient: the vast majority of paths will not intersect the atom, and will thus not contribute to the renormalized potential.…”

Section: B Casimir-polder Energiesmentioning

confidence: 99%

“…x(t) (25) for the TM polarization, where only the coordinate x 0 is elided in the notation • • • x(t) that denotes an ensemble average over vector Brownian bridges x(t) starting and returning to x 0 , and…”

Section: A Casimir Energies and Renormalizationmentioning

confidence: 99%

“…al showed how to apply the worldline method to computing Casimir energies for a scalar field coupled to a background potential, which models the material bodies [18,[21][22][23][24]. More recently, this method has been extended to computing stress-energy tensors for scalar fields, with applications to computing Casimir energies [25,26]. Since the formalism is not specific to any particular geometry, it serves as a method for numerically computing Casimir energies in arbitrary geometries.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

2016

View full text Add to dashboard Cite

We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric (TE) polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte-Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. While these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.

show abstract

Energy-Momentum Tensors With Worldline Numerics

Cited by 6 publications

References 21 publications

Worldline formalism for a confined scalar field

Worldline formalism for a confined scalar field

Propagator from nonperturbative worldline dynamics

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

Contact Info

Product

Resources

About