Particle creation and annihilation at interior boundaries: one-dimensional models

Keppeler, Stefan; Sieber, Martin

doi:10.1088/1751-8113/49/12/125204

Cited by 21 publications

(29 citation statements)

References 42 publications

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“…Let TeTu16,KeSi16,Gal16,DGTTZ17]. Introductory presentations of the kind of models considered here can be found in [TeTu15,TeTu16], and the physical motivation is discussed in [TeTu15].…”

Section: Introductionmentioning

confidence: 99%

“…6] considered IBCs for boundaries of codimension 1 (whereas the boundary relevant here has codimension 3) and did not provide rigorous results. Keppeler and Sieber [KeSi16] described a physical reasoning leading to IBCs and discussed IBCs in 1 space dimension (though not rigorously). Galvan [Gal16] suggested another approach towards a well defined Hamiltonian that has strong parallels to the IBC approach.…”

Section: Introductionmentioning

confidence: 99%

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Particle Creation at a Point Source by Means of Interior-Boundary Conditions

Schmidt

Lampart

Teufel

et al. 2018

Math Phys Anal Geom

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We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cutoff (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC. MSC: 81T10, 81Q10, 47F05. Key words: Ultraviolet divergence problem; renormalization in quantum field theory; self-adjoint Hamiltonian; self-adjoint extensions of the Laplace operator; particle-position representation; ultraviolet cut-off.

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“…Let TeTu16,KeSi16,Gal16,DGTTZ17]. Introductory presentations of the kind of models considered here can be found in [TeTu15,TeTu16], and the physical motivation is discussed in [TeTu15].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

Schmidt

Lampart

Teufel

et al. 2018

Math Phys Anal Geom

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“…Previous works [26,27,21,22,8,11,12,30] have focused on this relation of IBCs and non-relativistic (or pseudo-relativistic) Hamiltonians with particle creation and annihilation operators. It has been shown for simple models that understanding the creation part of the Hamiltonian as defining an IBC allows to make these models rigorous without the need for renormalization, which is usually required to treat the UV divergence.…”

Section: Introductionmentioning

confidence: 99%

Multi-time formulation of particle creation and annihilation via interior-boundary conditions

Lienert

Nickel

2019

Rev. Math. Phys.

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Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of linear conditions that relate the wave functions of two sectors of Fock space: ψ (n) (p) at an interior point p and ψ (n+m) (q) at a boundary point q, typically a collision configuration. Here, we extend IBCs to the relativistic case. To do this, we make use of Dirac's concept of multi-time wave functions, i.e., wave functions ψ(x 1 , ..., x N ) depending on N space-time coordinates x i for N particles. This provides the manifestly covariant particle-position representation that is required in the IBC approach. In order to obtain rigorous results, we construct a model for Dirac particles in 1+1 dimensions that can create or annihilate each other when they meet. Our main results are an existence and uniqueness theorem for that model, and the identification of a class of IBCs ensuring local probability conservation on all Cauchy surfaces. Furthermore, we explain how these IBCs relate to the usual formulation with creation and annihilation operators. The Lorentz invariance is discussed and it is found that apart from a constant matrix (which is required to transform in a certain way) the model is manifestly Lorentz invariant. This makes it clear that the IBC approach can be made compatible with relativity.

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“…There, rigorous models of interaction by boundary conditions have been constructed. There is some connection to the new concept of interior-boundary conditions by Teufel and Tumulka, which has so far been used to formulate certain non-relativistic QFT models without divergences [12,13,14]. It is an open but very interesting question if the method of interior-boundary conditions can help to formulate mathematically well-defined models of particle creation and annihilation in the multi-time formalism.…”

Section: Introductionmentioning

confidence: 99%

Consistency of multi-time Dirac equations with general interaction potentials

Deckert

Nickel

2016

Journal of Mathematical Physics

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In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under smoothness assumptions of possible solutions we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincaré invariance. We conclude that in this sense Dirac's multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.

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Particle creation and annihilation at interior boundaries: one-dimensional models

Cited by 21 publications

References 42 publications

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

Multi-time formulation of particle creation and annihilation via interior-boundary conditions

Consistency of multi-time Dirac equations with general interaction potentials

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