The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave

Finster, Felix; Reintjes, Moritz

doi:10.1007/s00023-017-0557-2

Cited by 3 publications

(3 citation statements)

References 37 publications

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“…In general, it is not clear if the state ω FP will be Hadamard or not. However, there are already explicit cases [FMR16,FiRe17] in which the construction is known to enjoy this property.…”

Section: Fermionic Projectormentioning

confidence: 99%

“…Remark 4.8. (i) The hypothesis of Theorem 4.7 are satisfied in Minkowski spacetime in the presence of a time-dependent external field [FMR16] and of a plane electromagnetic wave [FiRe17]. (ii) Variations on the construction of ω mFP can be obtained by varying the spectral function χ in the definition of Π mF P .…”

Section: New Classes Of Fermionic Projectorsmentioning

confidence: 99%

“…The net advantage of this construction is its independence from any structural property of the underlying background, such as the existence of specific Killing fields. This method has been successfully applied in [FMR16,FiRe17] to construct a distinguished Hadamard state for a Dirac field on Minkowski spacetime, in the presence of an external time-dependent potential, subject to suitable technical constraints. Despite these successes, an undeniable limitation of this method is the intrinsic difficulty of proving that the strong mass oscillation property holds true.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Drago

Murro

2017

Lett Math Phys

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Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in [FiRe16]. This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built.

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“…In general, it is not clear if the state ω FP will be Hadamard or not. However, there are already explicit cases [FMR16,FiRe17] in which the construction is known to enjoy this property.…”

Section: Fermionic Projectormentioning

confidence: 99%

Section: New Classes Of Fermionic Projectorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Drago

Murro

2017

Lett Math Phys

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The Fermionic Signature Operator in the Exterior Schwarzschild Geometry

Finster

Röken

2019

Ann. Henri Poincaré

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The structure of the solution space of the Dirac equation in the exterior Schwarzschild geometry is analyzed. Representing the space-time inner product for families of solutions with variable mass parameter in terms of the respective scalar products, a so-called mass decomposition is derived. This mass decomposition consists of a single mass integral involving the fermionic signature operator as well as a double integral which takes into account the flux of Dirac currents across the event horizon. The spectrum of the fermionic signature operator is computed. The corresponding generalized fermionic projector states are analyzed.

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A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes

Finster

Much

2022

Ann. Henri Poincaré

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The bosonic signature operator is defined for Klein–Gordon fields and massless scalar fields on globally hyperbolic Lorentzian manifolds of infinite lifetime. The construction is based on an analysis of families of solutions of the Klein–Gordon equation with a varying mass parameter. It makes use of the so-called bosonic mass oscillation property which states that integrating over the mass parameter generates decay of the field at infinity. We derive a canonical decomposition of the solution space of the Klein–Gordon equation into two subspaces, independent of observers or the choice of coordinates. This decomposition endows the solution space with a canonical complex structure. It also gives rise to a distinguished quasi-free state. Taking a suitable limit where the mass tends to zero, we obtain corresponding results for massless fields. Our constructions and results are illustrated in the examples of Minkowski space and ultrastatic spacetimes.

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The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave

Cited by 3 publications

References 37 publications

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

The Fermionic Signature Operator in the Exterior Schwarzschild Geometry

A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes

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