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

International Journal of Modern Physics A

THE SPIN-STATISTICS THEOREM ON A CIRCLE

Charilaos Aneziris

Published Nov 30, 1991• 1 citation
Publisher

Abstract

Recently, there has been a certain interest in the statistics of identical particles on a one-dimensional space. In this paper we extend this discussion to a circle by allowing the existence of antiparticles in addition to particles, and to creation-annihilation processes. This leads to much more complicated possibilities for statistics due to the change of the appropriate fundamental group.

DOI
10.1142/s0217751x91002380

Related papers

A TOPOLOGICAL SPIN-STATISTICS THEOREM OR A USE OF THE ANTIPARTICLE

A. P. Balachandran, Alan Daughton, Z.-C. GU +3 more

A spin-statistics theorem for spinning particles in ℝd is proved without using relativity or field theory, but assuming the existence of antiparticles. The theorem excludes non-abelian statistics such as parastatistics of order 2 and more for d≥3 and statistics based on nonabelian representations of the braid groups for d=2.

Modern Physics Letters A•Aug 20, 1990•31 citations

A topological spin-statistics theorem or a use of the antiparticle

A. P. Balachandran, Alan Daughton, Zixuan Gu +3 more

A spin-statistics theorem for spinning particles in d is proved without using relativity or field theory, but assuming the existence of antiparticles. The theorem excludes nonabelian statistics such as parastatistics of order 2 and more for d ⩾ 3 and statistics based on nonabelian representations of the braid groups for d = 2.

Physica Scripta•Jan 1, 1991•4 citations

Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles

Takafumi Kita

A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $π$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.

quant-pharXiv:2512.12071•Dec 16, 2025•0 citations

SPIN–STATISTICS THEOREMS WITHOUT RELATIVITY OR FIELD THEORY

A. P. Balachandran, Alan Daughton, Z.-C. GU +3 more

Conventional proofs of the spin–statistics theorem either use relativistic quantum field theory or concern field theory solitons. We here construct new proofs of this theorem for spinning particles. They are extensions of previous work on spinless particles and require neither relativity nor field theory. They do, however, assume certain continuity conditions involving the existence of antiparticles. Non-Abelian statistics, such as parastatistics and braid statistics of order 2 or more, are excluded in our framework.

International Journal of Modern Physics A•Jul 10, 1993•39 citations

SPIN-STATISTICS THEOREM AND GEOMETRIC QUANTIZATION

Charis Anastopoulos

We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantization procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the nonrelativistic domain (in fact for any symmetry group including internal symmetries) by requiring that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates — the exchange then arises from suitable change of coordinate system. We then examine our construction in the geometric and the coherent-state-path-integral quantization schemes. In the appendix we apply our results to exotic systems exhibiting continuous "spin" and "fractional statistics." This gives novel and unusual forms of the spin-statistics relation.

arXiv:quant-ph/0110169•International Journal of Modern Physics A•Feb 20, 2004•5 citations

STATISTICS FOR q-COMMUTATOR IN THE CASE OF qs+1=1

Yaping Yang, Shuangyuan Xie, WEIGUO FENG +1 more

In this letter, we introduce a new statistics to describe particles whose creation and annihilation operators satisfy the relation aa†-qa†a=1 in the case of qs+1=1.

Modern Physics Letters A•Apr 10, 1998•6 citations
Recently, there has been a certain interest in the statistics of identical particles on a one-dimensional space. In this paper we extend this discussion to a circle by allowing the existence of antiparticles in addition to particles, and to creation-annihilation processes. This leads to much more complicated possibilities for statistics due to the change of the appropriate fundamental group.
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a πππ-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.
Conventional proofs of the spin–statistics theorem either use relativistic quantum field theory or concern field theory solitons. We here construct new proofs of this theorem for spinning particles. They are extensions of previous work on spinless particles and require neither relativity nor field theory. They do, however, assume certain continuity conditions involving the existence of antiparticles. Non-Abelian statistics, such as parastatistics and braid statistics of order 2 or more, are excluded in our framework.
We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantization procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the nonrelativistic domain (in fact for any symmetry group including internal symmetries) by requiring that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates — the exchange then arises from suitable change of coordinate system. We then examine our construction in the geometric and the coherent-state-path-integral quantization schemes. In the appendix we apply our results to exotic systems exhibiting continuous "spin" and "fractional statistics." This gives novel and unusual forms of the spin-statistics relation.