Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

Gravejat, Philippe; Hainzl, Christian; Lewin, Mathieu; Séré, Éric

doi:10.1007/s00205-012-0609-1

Cited by 17 publications

(24 citation statements)

References 41 publications

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“…The complicated form of this expression is largely due to the greater number of regularising terms as compared to [11]. The response of the positive energy states is given by…”

Section: The Stability Of Homogeneous Systemsmentioning

confidence: 99%

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Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

Lampart

Lewin

2016

Ann. Henri Poincaré

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We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regularised vacuum energy. The leading order of this expansion is given by a classical formula due to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous proof. We then discuss applications to the non-relativistic large-coupling limit of an interacting system, and to the stability of homogeneous systems.

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“…The complicated form of this expression is largely due to the greater number of regularising terms as compared to [11]. The response of the positive energy states is given by…”

Section: The Stability Of Homogeneous Systemsmentioning

confidence: 99%

“…As we said, the regularisation used in (1) is not the only possible choice. Following [11], one can also consider the Pauli-Villars energy…”

Section: Introductionmentioning

confidence: 99%

Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

Lampart

Lewin

2016

Ann. Henri Poincaré

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“…The issue of the unidentified phase particularly concerns the so-called phenomenon of "vacuum polarization" as well as the dynamical description of pair creation processes for which only a few rigorous treatments are available; e.g., see [13] for vacuum polarization in the Hartree-Fock approximation for static external sources, [17] for adiabatic pair creation, and for a more fundamental approach the so-called "Theory of Causal Fermion Systems" [7,8,9], which is based on a reformulation of quantum electrodynamics by means of an action principle.…”

Section: Discussionmentioning

confidence: 99%

External Field QED on Cauchy Surfaces for Varying Electromagnetic Fields

Deckert

Merkl

2016

Commun. Math. Phys.

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Investigations were performed with S. Vafaeisefat [l, 41 on the mechanism of spontaneous chi-ral symmetry breaking via extenal fields in QED, especially by computer calculation using the Schwinger proper-time formalism in a density of states type of simulations. Some of the most significant results obtained include: the precise determination of the the parameter space widths for the gaussians in which one observes chiral symmetry breaking as defined by a non-zero expectation value for the fedonbilinear field expression; and the appropriate values for the parameters so that one also obtains spontaneous chiral symmetry breaking in a fully four-dimensional configuration produced by colliding same-sign charges. Our results provide strong evidence of a generic effect of such field configurations, which consitute a remarkable new phenomenon in quantum field theory. Our results allow us to estimate the minimum field strength required to induce spontaneous chiral symmetry breaking. The extension of these results to SU(2) non-abelian gauge theory was initiated with J. Cannellos at Buffalo, and E. Ferrer and V. Incera at S U N Y Fredonia, and is in progress. Strings, Conformal Field Theories, and Toda Field Theories N o investigations of affine Toda field theories were carried out with 2. Zhu. In the first investigation [2], Hirota's method was used to construct multi-soliton and plane-wave solutions for affine Toda field theories with imaginary coupling. In the second [3], it was shown that there are infinitely many topological solitons in any given complex affine Toda theories and most of them have complex energy density. When we require the energy density of the solitons to be real, we find that the reality condition is related to a simple "pairing condition." Unfortunately, rather few soliton solutions in these theories survive the reality constraint, especially if one also demands positivity. The resulting implications for the physical applicability of these theories were investigated. Cosmological Neutrino Condensates With A. Chodos [5], we investigated the possibility that neutrinos form superfluid-type condensates in background cosmological densities. Such condensates could give rise to small neutrino masses and splittings, as well as an important contribution, perhaps, to the cosmological constant. We discussed various channels in the context of the standard model. Many of these do not support a condensate, but some mixed-flavor channels do. We also suggested a new interaction, acting only among neutrinos, that could induce a neutrino Majorana mass of order 1 eV. Our conclusions can be enumerated as 'follows: (i) There is no attractive channel in the purely neutrino sector of the standard model; (ii) The addition of charged leptons leads to attraction in the flavor off-diagonal channels, but a pairing instability occurs only if the Fermi momenta of the neutrino and I DOE Patent Clearance Granted Mark t ? Dvorscak Office of Intellectual Props $.Law DOE Chicago Operations frce cf.fl.ol Date v-L-630) 252-2393-mail: ...

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“…However, quantities such as the charge-current density depend manifestly on this unidentified phase. In particular, this concerns the so-called phenomenon of vacuum polarization but also the dynamical description of pair creation processes for which so far only a few rigorous treatments are available; see [GHLS13] for vacuum polarization in the Hartree-Fock approximation for static external sources and [DP07] for adiabatic pair creation. The involved degrees of freedom can be reduced further by imposing the Bogolyubov causality condition [BS59,(17.30)] or more or less equivalently by implementing second-quantized evolution maps between Fock spaces associated to space-like Cauchy hypersurfaces, which is the content of a follow-up work.…”

Section: Introductionmentioning

confidence: 99%

Dirac equation with external potential and initial data on Cauchy surfaces

Deckert¹,

Merkl²

2014

Journal of Mathematical Physics

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With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincaré group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener-and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindelöf argument this evolution map is generalized to the Dirac evolution including the external potential. For the latter we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide another proof of the well-known existence and uniqueness of classical solutions and their causal structure.

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Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

Cited by 17 publications

References 41 publications

Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

External Field QED on Cauchy Surfaces for Varying Electromagnetic Fields

Dirac equation with external potential and initial data on Cauchy surfaces

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