In quantum mechanics, superselection extends the concept of selection rules.
Superselection rules are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables.[1]
It was originally introduced by Gian Carlo Wick, Arthur Wightman, and Eugene Wigner to impose additional restrictions to quantum theory beyond those of selection rules.
Mathematically speaking, two quantum states and are separated by a selection rule if for the given Hamiltonian , while they are separated by a superselection rule if for all physical observables . Because no observable connects and they cannot be put into a quantum superposition , and/or a quantum superposition cannot be distinguished from a classical mixture of the two states. It also implies that there is a classically conserved quantity that differs between the two states.[2]
A superselection sector is a concept used in quantum mechanics when a representation of a *-algebra is decomposed into irreducible components. It formalizes the idea that not all self-adjoint operators are observables because the relative phase of a superposition of nonzero states from different irreducible components is not observable (the expectation values of the observables can't distinguish between them).
^Bartlett, Stephen D.; Rudolph, Terry; Spekkens, Robert W. (April–June 2007). "Reference frames, superselection rules, and quantum information". Reviews of Modern Physics. 79 (2): 555–606. arXiv:quant-ph/0610030. Bibcode:2007RvMP...79..555B. doi:10.1103/RevModPhys.79.555. S2CID 118880279.
In quantum mechanics, superselection extends the concept of selection rules. Superselection rules are postulated rules forbidding the preparation of quantum...
frame is mathematically equivalent to superselection rules. This is a powerful statement because superselection rules have long been thought to have axiomatic...
Known for Co-founder of PsiQuantum, PBR theorem, One-way quantum computer, superselection, Boson Sampling Scientific career Thesis Dressing an Atom in a Field...
In quantum mechanics, einselections, short for "environment-induced superselection", is a name coined by Wojciech H. Zurek for a process which is claimed...
chromodynamics is an ordering transition; it is discussed in terms of superselection. Entropy Topological order Impurity superstructure (physics) H Kleinert:...
collaboration with Rudolf Haag. With John E. Roberts and Haag, he examined superselection rules in the algebraic quantum field theory, providing the first proof...
book. Together with Eugene Wigner and Gian-Carlo Wick, he introduced superselection rules and studied the representations of commutator and anti-commutator...
ourselves to a superselection sector. The cyclicity of the vacuum demanded by the Wightman axioms means that they describe only the superselection sector of...
quantum-mechanical description of the cat-and-particle system must include a superselection rule.: 51 ) "Wigner's friend" is a thought experiment intended to make...
ISSN 0003-4916. Wick, G. -C.; Wightman, A. S.; Wigner, Eugene P. (1970-06-15). "Superselection Rule for Charge". Physical Review D. 1 (12). American Physical Society...
perpendicular to the surface will be observed in the vibrational spectrum. Superselection rule Spin-forbidden reactions Singlet fission Harris & Bertolucci, p...
established that the magnetization in the Ising model eventually defines superselection sectors, separated domains not linked by finite fluctuations. Kramers...
coherence) with each other. This is called "environmentally-induced superselection", or einselection. The decohered elements of the system no longer exhibit...
representations. Each irreducible representation (up to equivalence) is called a superselection sector. We assume there is a pure state called the vacuum such that...
Rudolph, Terry; Spekkens, Robert W. (April–June 2007). "Reference frames, superselection rules, and quantum information". Reviews of Modern Physics. 79 (2):...
with anti-de Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative background-independent theory. But it would still...
infinity, which is determined by the velocity of a point charge, defines superselection sectors for the particle's Hilbert space. This is unlike the usual Fock...
Hamiltonian cannot be split into a free and an interacting part within a superselection sector. Moreover, even if in the Schrödinger picture the Hamiltonian...
or temperature is raised above T c {\displaystyle T_{c}} . See also superselection sector The main mathematical tools to study critical points are renormalization...
different physics. In other words, the Hilbert space decomposes into superselection sectors since expectation values of gauge invariant operators between...
)=g[X(\sigma ,\tau )]} For each conjugacy class of G, we have a different superselection sector (wrt the worldsheet). The conjugacy class consisting of the identity...
whose integral depends only upon the homotopy class; this results in superselection sectors in the quantised model. In (1 + 1)-dimensional spacetime, a...
Doplicher and John E. Roberts, elucidated the possible structure of the superselection sectors of the observables in theories with short-range forces. Sectors...
(2006). From Micro to Macro Quantum Systems, (A Unified Formalism with Superselection Rules and Its Applications). World Scientific. ISBN 978-1-86094-625-7...
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