The four-dimensional position operator in theories with broken conformal symmetry

Haba, Z.

doi:10.1007/bf02730001

Cited by 4 publications

(1 citation statement)

References 16 publications

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“…In [17,18] the charges of the special conformal transformations have become candidates for a relativistic four position operator. From a different point of view this has also been studied in [19][20][21]. In detail we will discuss below [22].…”

Section: Embedding Our Approachmentioning

confidence: 99%

Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

Pottel¹,

Sibold²

2016

Phys. Rev. D

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For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operators P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit m 2 → 0 on the one hand, on the other from conformal transformations. Crucial is the norm problem of the states on which the Q's act: they determine eventually how many independent conjugate pairs exist. It is intriguing that (light-) wedge variables and hence the wedge-local case seems to be preferred. 1

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Section: Embedding Our Approachmentioning

confidence: 99%

Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

Pottel¹,

Sibold²

2016

Phys. Rev. D

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Coherent States on the Conformal Group and Position Operator

Haba¹

1977

Group Theoretical Methods in Physics

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Localizing the relativistic electron

Bracken

Melloy

1999

J. Phys. A: Math. Gen.

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A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the 4-vector density (ρ(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive-energy states. A suitable spin operator can be diagonalized at the same time.

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The four-dimensional position operator in theories with broken conformal symmetry

Cited by 4 publications

References 16 publications

Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

Coherent States on the Conformal Group and Position Operator

Localizing the relativistic electron

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