Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Interpretational difficulties in quantum field theory

Piotr Krekora, Qichang C. Su, R. Grobe

Published Feb 23, 2006• 41 citations
Publisher

Abstract

Based on space-time-resolved solutions to relativistic quantum field theory we illustrate interpretational difficulties in associating field-theoretical quantities with properties of particles. These difficulties are related to the fact that the definition of the spatial probability density of particles depends on the choice of the Hilbert subspace on which the field operator is projected. We illustrate these problems by analyzing pair-production probabilities and spatial densities for the electron-positron dynamics associated with a spatially localized subcritical potential that is turned on and off in time.

DOI
10.1103/physreva.73.022114

Related papers

Space-time resolved quantum field theory

Piotr Krekora, Qichang C. Su, R. Grobe

Using space-time resolved solutions in relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum and resolve the Klein-paradox. We show that there are in principle no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also argue that quantum field theory prohibits the occurrence of Zitterbewegung for an electron in contrast to claims found in textbooks.

Frontiers in Optics•Jan 1, 2004•0 citations

Relativistic Electron Localization and the Lack ofZitterbewegung

Piotr Krekora, Qichang C. Su, R. Grobe

Using space-time resolved solutions to relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum. For early times the entangled electron-positron wave function can be obtained analytically. We show that there are, in principle, no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also find that quantum field theory prohibits the occurrence of Zitterbewegung for an electron.

Physical Review Letters•Jul 23, 2004•100 citations

Localization of particles in quantum field theory

W. Westra

We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is difficult if particle localization is defined using the Newton-Wigner position operator as it is non-local and non-covariant. An alternative bilinear covariant position operator is discussed which incorporates a time operator that can be exponentiated to a unitary operator. Moreover, it satisfies an algebra that unifies special relativity and quantum mechanics and has the same form for particles with spin. Higher power position operators are derived which yield Heisenberg's uncertainty relations. Our ideas are illustrated with a relativistic wave function whose probability density can be perfectly localized.

arXiv:1012.3472•Dec 15, 2010•3 citations

On the construction of macroscopically local relativistic quantum theories

Jon R. Nance

"The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these ""quasilocal"" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed."

•Jan 1, 1966•0 citations

Quantum time and spatial localization in relativistic quantum mechanics

Von Zuben, Francis Stephen Geisler

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles, and the dependence of their localization on the motion of the observer, are analyzed in the context of the theory of constraints. Time and energy operators are introduced for the free relativistic particle, and a parametrization invariant formulation is obtained through Dirac constraint theory. The resulting description is of a system constrained in momentum and energy, but not in position or time, for which observables are constants of the motion. The Klein-Gordon equation is recovered on a physical Hilbert space, constructed via integration over the proper time from an augmented Hilbert space, wherein time and energy are dynamical variables...

•Nov 1, 1999•1 citation

A realistic interpretation of the density matrix

A. Raiteri

A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an "objective" extra space dimension. "Particle" solutions are found, which are perfectly localized both in position space and in momentum space (the position and momentum operators commute in the density matrix representation); definitions for all observable quantities are given and the values associated to the "particle" solutions are the correct ones, both for the non-relativistic and the relativistic case. Finally, a non-linear interaction (the electromagnetic one) is introduced in an attempt to single out the "particle" solutions of the Dirac equation from all other solutions; the dynamical evolution of the electromagnetic field is described by the classical (unquantized) Maxwell equations.

•Dec 4, 1998•0 citations
Based on space-time-resolved solutions to relativistic quantum field theory we illustrate interpretational difficulties in associating field-theoretical quantities with properties of particles. These difficulties are related to the fact that the definition of the spatial probability density of particles depends on the choice of the Hilbert subspace on which the field operator is projected. We illustrate these problems by analyzing pair-production probabilities and spatial densities for the electron-positron dynamics associated with a spatially localized subcritical potential that is turned on and off in time.
Using space-time resolved solutions in relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum and resolve the Klein-paradox. We show that there are in principle no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also argue that quantum field theory prohibits the occurrence of Zitterbewegung for an electron in contrast to claims found in textbooks.
Using space-time resolved solutions to relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum. For early times the entangled electron-positron wave function can be obtained analytically. We show that there are, in principle, no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also find that quantum field theory prohibits the occurrence of Zitterbewegung for an electron.
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is difficult if particle localization is defined using the Newton-Wigner position operator as it is non-local and non-covariant. An alternative bilinear covariant position operator is discussed which incorporates a time operator that can be exponentiated to a unitary operator. Moreover, it satisfies an algebra that unifies special relativity and quantum mechanics and has the same form for particles with spin. Higher power position operators are derived which yield Heisenberg's uncertainty relations. Our ideas are illustrated with a relativistic wave function whose probability density can be perfectly localized.
"The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these ""quasilocal"" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed."
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles, and the dependence of their localization on the motion of the observer, are analyzed in the context of the theory of constraints. Time and energy operators are introduced for the free relativistic particle, and a parametrization invariant formulation is obtained through Dirac constraint theory. The resulting description is of a system constrained in momentum and energy, but not in position or time, for which observables are constants of the motion. The Klein-Gordon equation is recovered on a physical Hilbert space, constructed via integration over the proper time from an augmented Hilbert space, wherein time and energy are dynamical variables...
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an "objective" extra space dimension. "Particle" solutions are found, which are perfectly localized both in position space and in momentum space (the position and momentum operators commute in the density matrix representation); definitions for all observable quantities are given and the values associated to the "particle" solutions are the correct ones, both for the non-relativistic and the relativistic case. Finally, a non-linear interaction (the electromagnetic one) is introduced in an attempt to single out the "particle" solutions of the Dirac equation from all other solutions; the dynamical evolution of the electromagnetic field is described by the classical (unquantized) Maxwell equations.