Distinguishable- and indistinguishable-particle descriptions of systems of identical particles

W. M. De Muynck

doi:10.1007/bf01807861

Distinguishable- and indistinguishable-particle descriptions of systems of identical particles

International Journal of Theoretical Physics ◽

10.1007/bf01807861 ◽

1975 ◽

Vol 14 (5) ◽

pp. 327-346 ◽

Cited By ~ 15

Author(s):

W. M. De Muynck

Keyword(s):

Identical Particles ◽

Indistinguishable Particle

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Identical Particles and Second Quantization: Occupation Number Representation

10.1093/oso/9780198791942.003.0002 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Occupation Number ◽

Annihilation Operator ◽

Pauli Exclusion Principle ◽

Exclusion Principle ◽

Number Representation ◽

Second Quantization ◽

Identical Particles ◽

Fundamental Properties ◽

Minimum Uncertainty ◽

Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

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Locality and entanglement of indistinguishable particles

Scientific Reports ◽

10.1038/s41598-021-94991-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Till Jonas Frederick Johann ◽

Ugo Marzolino

Keyword(s):

Quantum Mechanics ◽

Quantum Correlation ◽

Indistinguishable Particle ◽

Local Operators

AbstractEntanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies. While entanglement theory is well settled for distinguishable particles, there are five inequivalent approaches to entanglement of indistinguishable particles. We analyse the different definitions of indistinguishable particle entanglement in the light of the locality notion. This notion is specified by two steps: (i) the identification of subsystems by means of their local operators; (ii) the requirement that entanglement represent correlations between the above subsets of operators. We prove that three of the aforementioned five entanglement definitions are incompatible with any locality notion defined as above.

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Decay amplitudes to three hadrons from finite-volume matrix elements

Journal of High Energy Physics ◽

10.1007/jhep04(2021)113 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Maxwell T. Hansen ◽

Fernando Romero-López ◽

Stephen R. Sharpe

Keyword(s):

Finite Volume ◽

Decay Amplitude ◽

Weak Decay ◽

Matrix Elements ◽

Isospin Breaking ◽

Final State ◽

Identical Particles ◽

Hadron Decay ◽

Finite State ◽

Particle Decays

Abstract We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

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