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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Superselection Rule for Charge

G. C. Wick, Arthur S. Wightman, Eugene Paul Wigner

Published Jun 15, 1970• 91 citations
Publisher

Abstract

The customary notion of superselection rule stipulates the vanishing of those matrix elements of the density matrix that connect states separated by the superselection rule, i.e., the relative phases of which are, according to the superselection rule, meaningless. It is shown that, if any two states for which an additive conserved quantity has different values are separated for all physical systems by a superselection rule at one time, the separation will persist for all times. It is concluded that the states with different electric (or baryonic) charges are so separated. The reason for the difference between electric charge and other additive conserved quantities, such as momentum, is brought out.

DOI
10.1103/physrevd.1.3267

Related papers

Charge Superselection Rule

Yakir Aharonov, Leonard Susskind

Questions concerning superselection rules are considered. Two experiments are discussed. In the first, coherent superpositions of different angular-momentum states are constructed. In the second, coherent superpositions of states with different charge are constructed in complete analogy with the angular-momentum case. We suggest that, contrary to a widespread belief, interference may be possible between states with different charges.

Physical Review•Mar 25, 1967•242 citations

Critical Comment on the Nonexistence of the Charge Superselection Rule

Yasuo Yoshihuku

Aharonov and Susskind denied the concept of the superselection rules, and suggested the experimental feasibility of measuring interference between states with different charges. Their reasoning is shown to be incorrect.

Progress of Theoretical Physics•Jun 1, 1972•1 citation

Superselection Rules from Measurement Theory

Shogo Tanimura

In quantum theory, physically measurable quantities of a microscopic system are represented by self-adjoint operators. However, not all of the self-adjoint operators correspond to measurable quantities. The superselection rule is a criterion to distinguish measurable quantities. Any measurable quantity must obey the superselection rules. By contraposition, any quantity which does not obey the superselection rules cannot be measured. Although some of superselection rules were proved, the raizon d'être of the superselection rules has been still obscure. In this paper we deduce the superselection rules from an assumption on symmetry property of measurement process. We introduce the notion of covariant indicator, which is a macroscopic observable whose value indicates the value of a microscopic object observable. We prove that if an object system has a quantity that is conserved during the measurement process, other quantities that do not commute with the conserved quantity are non-measurable by the covariant indicator. Our derivation of superselection rules is compared with the uncertainty relation under the restriction by a conservation law. An implication of the color superselection rule for the color confinement is discussed. It is also argued that spontaneous symmetry breaking enables a measurement that the superselection rule prohibits.

arXiv:1112.5701•Dec 24, 2011•4 citations

States, Symmetries and Superselection

Domenico Giulini

The process of dynamical decoherence may cause apparent superselection rules, which are sometimes called `environmentally induced' or `soft'. A natural question is whether such dynamical processes are eventually also responsible for at least some of the superselection rules which are usually presented as fundamentally rooted in the kinematical structure of the theory (so called `hard' superselection rules). With this question in mind, I re-investigate two well known examples where superselection rules are usually argued to rigorously exist within the given mathematical framework. These are (1) the Bargmann superselection rule for the total mass in Galilei invariant quantum mechanics and (2) the charge superselection rule in quantum electrodynamics. I argue that, for various reasons, the kinematical arguments usually given are not physically convincing unless they are based on an underlying dynamical process.

arXiv:quant-ph/9906108•Jun 28, 1999•3 citations

Charge superselection rule does not rule out pure states of subsystems to be coherent superpositions of states with different charges

Shimizu, Akira, Takayuki Miyadera

We consider a huge quantum system that is subject to the charge superselection rule, which requires that any pure state must be an eigenstate of the total charge. We regard some parts of the system as "subsystems," and the rest as an environment E. We assume that one does not measure anything of E, i.e., one is only interested in observables of the subsystems. We show that there exist states with the following properties: (i) Its reduced density operator is completely equivalent to a vector state of the subsystems for any gauge-invariant observable of the subsystems. (ii) The vector state is a simple product of vector states of individual subsystems, each of which is not an eigenstate of the charge of each subsystem. Furthermore, one can associate to each subsystem its vector state, which is a pure state, and observables which are not necessarily gauge invariant in each subsystem. These results justify taking (a) superpositions of states with different charges, and (b) non-gauge-invariant operators, such as the order parameter of the breaking of the gauge symmetry, as observables, for subsystems.

arXiv:cond-mat/0102429•Feb 23, 2001•1 citation

Superselection rules, bosonization duality in 1 + 1 dimensions, and momentum-space entanglement

Matheus H. Martins Costa, Flavio S. Nogueira, Jeroen van den Brink

We investigate the effects of the presence of conserved charges on the momentum-space entanglement of quantum field theories. We show that if a given model has superselection sectors, then it allows for different notions of momentum modes, each associated with a complete set of commuting observables. Applying this idea to investigate the entanglement of momentum degrees of freedom on both sides of the Abelian bosonization duality, we find that different tensor product partitions are mapped into each other and give explicit examples to sustain our findings. The conditions on which our conclusions may be generalized to other duality transformations, which require the introduction of a notion stricter than the most general possible, are laid and directions for further work are given. Published by the American Physical Society 2024

arXiv:2410.01908•Physical review. D/Physical review. D.•Nov 25, 2024•0 citations
The customary notion of superselection rule stipulates the vanishing of those matrix elements of the density matrix that connect states separated by the superselection rule, i.e., the relative phases of which are, according to the superselection rule, meaningless. It is shown that, if any two states for which an additive conserved quantity has different values are separated for all physical systems by a superselection rule at one time, the separation will persist for all times. It is concluded that the states with different electric (or baryonic) charges are so separated. The reason for the difference between electric charge and other additive conserved quantities, such as momentum, is brought out.
In quantum theory, physically measurable quantities of a microscopic system are represented by self-adjoint operators. However, not all of the self-adjoint operators correspond to measurable quantities. The superselection rule is a criterion to distinguish measurable quantities. Any measurable quantity must obey the superselection rules. By contraposition, any quantity which does not obey the superselection rules cannot be measured. Although some of superselection rules were proved, the raizon d'être of the superselection rules has been still obscure. In this paper we deduce the superselection rules from an assumption on symmetry property of measurement process. We introduce the notion of covariant indicator, which is a macroscopic observable whose value indicates the value of a microscopic object observable. We prove that if an object system has a quantity that is conserved during the measurement process, other quantities that do not commute with the conserved quantity are non-measurable by the covariant indicator. Our derivation of superselection rules is compared with the uncertainty relation under the restriction by a conservation law. An implication of the color superselection rule for the color confinement is discussed. It is also argued that spontaneous symmetry breaking enables a measurement that the superselection rule prohibits.
The process of dynamical decoherence may cause apparent superselection rules, which are sometimes called `environmentally induced' or `soft'. A natural question is whether such dynamical processes are eventually also responsible for at least some of the superselection rules which are usually presented as fundamentally rooted in the kinematical structure of the theory (so called `hard' superselection rules). With this question in mind, I re-investigate two well known examples where superselection rules are usually argued to rigorously exist within the given mathematical framework. These are (1) the Bargmann superselection rule for the total mass in Galilei invariant quantum mechanics and (2) the charge superselection rule in quantum electrodynamics. I argue that, for various reasons, the kinematical arguments usually given are not physically convincing unless they are based on an underlying dynamical process.
We consider a huge quantum system that is subject to the charge superselection rule, which requires that any pure state must be an eigenstate of the total charge. We regard some parts of the system as "subsystems," and the rest as an environment E. We assume that one does not measure anything of E, i.e., one is only interested in observables of the subsystems. We show that there exist states with the following properties: (i) Its reduced density operator is completely equivalent to a vector state of the subsystems for any gauge-invariant observable of the subsystems. (ii) The vector state is a simple product of vector states of individual subsystems, each of which is not an eigenstate of the charge of each subsystem. Furthermore, one can associate to each subsystem its vector state, which is a pure state, and observables which are not necessarily gauge invariant in each subsystem. These results justify taking (a) superpositions of states with different charges, and (b) non-gauge-invariant operators, such as the order parameter of the breaking of the gauge symmetry, as observables, for subsystems.
We investigate the effects of the presence of conserved charges on the momentum-space entanglement of quantum field theories. We show that if a given model has superselection sectors, then it allows for different notions of momentum modes, each associated with a complete set of commuting observables. Applying this idea to investigate the entanglement of momentum degrees of freedom on both sides of the Abelian bosonization duality, we find that different tensor product partitions are mapped into each other and give explicit examples to sustain our findings. The conditions on which our conclusions may be generalized to other duality transformations, which require the introduction of a notion stricter than the most general possible, are laid and directions for further work are given. Published by the American Physical Society 2024