Abstract We employ reduced density matrices to investigate the localization of relativistic particles within the framework of $$(1+1)$$ ( 1 + 1 ) -dimensional quantum field theory. In the case of bosons, we prove that scalar particles cannot be localized within any compact region, although they can be made arbitrarily close to localized states. For massless fermions, by exploiting properties of the reduced density matrices of coherent states, we show that the fermionic single-particle state which, under constructive bosonization, corresponds to a bosonic coherent state is strictly localized at a single spatial point; however, the energy of this state is infinite. Moreover, since the notion of spatial localization based on reduced density matrices is consistent with relativistic causality, even a particle with infinite energy that is localized at a single spatial point will neither spread outside the light cone nor propagate superluminally. Indeed, the explicit expression for the localized fermionic state derived in our work shows that a massless fermion can preserve its sharply localized profile while propagating at the speed of light, in full agreement with causality.

The European Physical Journal CMar 18, 20260 citations

arXiv:1903.07312 · Annals of Physics

On the coherent states for a relativistic scalar particle

K. Kowalski, Jakub Rembieliński, Jean‐Pierre Gazeau

Published Oct 22, 2018• 8 citations

arXiv HTML PDF

DOI: 10.1016/j.aop.2018.10.014

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Localization of relativistic particles

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Abstract We employ reduced density matrices to investigate the localization of relativistic particles within the framework of $(1+1)$ ( 1 + 1 ) -dimensional quantum field theory. In the case of bosons, we prove that scalar particles cannot be localized within any compact region, although they can be made arbitrarily close to localized states. For massless fermions, by exploiting properties of the reduced density matrices of coherent states, we show that the fermionic single-particle state which, under constructive bosonization, corresponds to a bosonic coherent state is strictly localized at a single spatial point; however, the energy of this state is infinite. Moreover, since the notion of spatial localization based on reduced density matrices is consistent with relativistic causality, even a particle with infinite energy that is localized at a single spatial point will neither spread outside the light cone nor propagate superluminally. Indeed, the explicit expression for the localized fermionic state derived in our work shows that a massless fermion can preserve its sharply localized profile while propagating at the speed of light, in full agreement with causality.Abstract We employ reduced density matrices to investigate the localization of relativistic particles within the framework of $$(1+1)$$ ( 1 + 1 ) -dimensional quantum field theory. In the case of bosons, we prove that scalar particles cannot be localized within any compact region, although they can be made arbitrarily close to localized states. For massless fermions, by exploiting properties of the reduced density matrices of coherent states, we show that the fermionic single-particle state which, under constructive bosonization, corresponds to a bosonic coherent state is strictly localized at a single spatial point; however, the energy of this state is infinite. Moreover, since the notion of spatial localization based on reduced density matrices is consistent with relativistic causality, even a particle with infinite energy that is localized at a single spatial point will neither spread outside the light cone nor propagate superluminally. Indeed, the explicit expression for the localized fermionic state derived in our work shows that a massless fermion can preserve its sharply localized profile while propagating at the speed of light, in full agreement with causality.

The European Physical Journal CMar 18, 20260 citations

Abstract We employ reduced density matrices to investigate the localization of relativistic particles within the framework of

(1+1)

( 1 + 1 ) -dimensional quantum field theory. In the case of bosons, we prove that scalar particles cannot be localized within any compact region, although they can be made arbitrarily close to localized states. For massless fermions, by exploiting properties of the reduced density matrices of coherent states, we show that the fermionic single-particle state which, under constructive bosonization, corresponds to a bosonic coherent state is strictly localized at a single spatial point; however, the energy of this state is infinite. Moreover, since the notion of spatial localization based on reduced density matrices is consistent with relativistic causality, even a particle with infinite energy that is localized at a single spatial point will neither spread outside the light cone nor propagate superluminally. Indeed, the explicit expression for the localized fermionic state derived in our work shows that a massless fermion can preserve its sharply localized profile while propagating at the speed of light, in full agreement with causality.