Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

Herdegen, Andrzej

doi:10.1063/1.532264

Cited by 26 publications

(102 citation statements)

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“…That mathematical technology also relies upon some ideas essentially due to Ashtekar [59] and that have also received attention for applications to electrodynamics [60,61] in asymptotically at spacetimes. Finally, a mathematically similar procedure was employed in [31] to prove the Hadamard property of some relevant states in a di erent physical context.…”

Section: Introductionmentioning

confidence: 99%

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Dappiaggi¹,

Moretti²,

Pinamonti³

2011

Advances in Theoretical and Mathematical Physics

138

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The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state, which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon e-print archive: http://lanl.arXiv.org/abs/0907.1034 CLAUDIO DAPPIAGGI ET AL.field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation.From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hörmander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.

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Section: Introductionmentioning

confidence: 99%

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Dappiaggi¹,

Moretti²,

Pinamonti³

2011

Advances in Theoretical and Mathematical Physics

138

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“…For currents with non-vanishing both future and past asymptotes J as the rhs of the second equation in (3.30) is the total charge. The radiation potential produced by the current J ∈ J as is completely determined byV (s, l) according to the formula [9] A(…”

Section: Spaces S κ κ+mentioning

confidence: 99%

“…We further develop the approach to the infrared problem initiated in our earlier papers (Ref. [9] and papers cited therein; see also [10]); this proposition may be regarded as an attempt at an algebraic formulation of an asymptotic dynamics respecting the long-range nature of electromagnetic field and Gauss' law. The term "asymptotic" is meant here in the sense used in the scattering theory, but the algebra is rather postulated then derived from a complete theory.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [9] the algebra was formulated in terms of independent asymptotic variables (the electromagnetic field part using the null infinity variables similar to those used by other authors before, as discussed in [9]; we do not use the conformal compactification technique of Penrose). Here we extend our discussion by including the issues of spacetime localization of fields and we formulate anew the interpretational issues involved.…”

Section: Introductionmentioning

confidence: 99%

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Infrared Problem and Spatially Local Observables in Electrodynamics

Herdegen

2008

Ann. Henri Poincaré

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An algebra previously proposed as an asymptotic field structure in electrodynamics is considered in respect of localization properties of fields. Fields are 'spatially local' -localized in regions resulting as unions of two intersecting (solid) lightcones: a future-and a past-lightcone. This localization remains in concord with the usual idealizations connected with the scattering theory. Fields thus localized naturally include infrared characteristics normally placed at spacelike infinity and form a structure respecting Gauss' law. When applied to the description of the radiation of an external classical current the model is free of 'infrared catastrophe'. *

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“…The need for nonlocality may be even more justified in case of non-observable fields, such as, e.g., the gauge potential in physical gauges. See [10] for a (nonlocal) model of asymptotic fields in QED; see also [11] for a more recent argument for nonlocality and some bibliographic remarks. However, we stress once more that our present results do not depend on our more specific motivation and include, in particular, local case.…”

Section: Introductionmentioning

confidence: 99%

On Energy-Momentum Transfer of Quantum Fields

Herdegen

2014

Lett Math Phys

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Abstract. We prove the following theorem on bounded operators in quantum field theory:is a function weakly decaying in spacelike directions, B k ± are creation/annihilation parts of an appropriate time derivative of B, G is any positive, bounded, non-increasing function in L 2 (R), and ν is any finite complex Borel measure; creation/annihilation operators may be also replaced by B k t with B k t ( p) = | p| kB ( p). We also use the notion of energymomentum scaling degree of B with respect to a submanifold (Steinmann-type, but in momentum space, and applied to the norm of an operator). These two tools are applied to the analysis of singularities ofB( p)G(P 0 ). We prove, among others, the following statement (modulo some more specific assumptions): outside p = 0 the only allowed contributions to this functional which are concentrated on a submanifold (including the trivial one-a single point) are Dirac measures on hypersurfaces (if the decay of D is not to slow).Mathematics Subject Classification (2010). 46L40, 81T05.

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Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

Cited by 26 publications

References 26 publications

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Infrared Problem and Spatially Local Observables in Electrodynamics

On Energy-Momentum Transfer of Quantum Fields

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