Extension of the spin-statistics theorem to nonlocal fields

Соловьев, Михаил Александрович

doi:10.1134/1.567736

Cited by 6 publications

(17 citation statements)

References 4 publications

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“…For simplicity, we are going to discuss the CPT and Spin-Statistics theorems only for the scalar field Φ(x). Ours results are corollaries of the Soloviev's Theorems generalizing the CPT invariance and Spin-Statistics connection for nonlocal field theories, and ours proofs follow directly from the chain of reasoning of [14]- [17].…”

Section: Proof Of the Cpt And Spin-statistics Theoremsmentioning

confidence: 88%

“…Then, we examine how essential are the locality of interactions and the microcausality axiom in order to reach a conclusion about the validity of the CPT and Spin-Statistics theorems in NCFT, in the case of only spatial non-commutativity -this choice preserves the unitarity [19] and the causality [20]. We show that both theorems hold within this environment if the postulate of microcausality suggested byÁlvarez-Gaumé and Vásquez-Mozo [6] is replaced with a condition implying the macrocausality as suggested by Soloviev [14]- [17]. This makes our proofs stronger than ones given bý Alvarez-Gaumé and Vásquez-Mozo [6], in the sense that our hypotheses are weaker.…”

Section: Introductionmentioning

confidence: 94%

“…Here, following Soloviev [14]- [17], we relax the condition (3.4) and introduce, as a substitute for the axiom of locality, the following axiom:…”

Section: Asymptotic Commutativitymentioning

confidence: 99%

“…In [12,13], Lücke overcame this problem using the analyticity properties of vacuum expectation values in the momentum space and analyzed the relevant envelopes of holomorphy. More recently, an alternative and elegant solution has been given by Soloviev [14,15,16] using the notion of the analytic wavefront set and a type of uniqueness theorem for distributions. For simplicity, we are going to discuss the CPT and Spin-Statistics theorems only for the scalar field Φ(x).…”

Section: Proof Of the Cpt And Spin-statistics Theoremsmentioning

confidence: 99%

“…The main purpose of this work is to show that, from a distributional-theoretical framework, the analysis ofÁlvarez-Gaumé and Vásquez-Mozo [6] on the extension of the Wightman axioms to the context of NCFT can be reformulated by adoption immediate of some ideas introduced by Soloviev [14]- [17], which are applicable to non-commutative quantum field models. Then, we examine how essential are the locality of interactions and the microcausality axiom in order to reach a conclusion about the validity of the CPT and Spin-Statistics theorems in NCFT, in the case of only spatial non-commutativity -this choice preserves the unitarity [19] and the causality [20].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A new derivation of the CPT and spin-statistics theorems in noncommutative field theories

Franco

Polito

2005

Journal of Mathematical Physics

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We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a possible violation of the CPT and Spin-Statistics theorems caused by nonlocality of the commutation relations [ x µ , x ν ] = iθ µν is investigated. In spite of this inherent nonlocality, we show that the modification aforementioned is sufficient to ensure the validity of these theorems for NCFT. We restrict ourselves to the simplest model of a scalar field in the case of only space-space non-commutativity.

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Section: Proof Of the Cpt And Spin-statistics Theoremsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 94%

“…Here, following Soloviev [14]- [17], we relax the condition (3.4) and introduce, as a substitute for the axiom of locality, the following axiom:…”

Section: Asymptotic Commutativitymentioning

confidence: 99%

Section: Proof Of the Cpt And Spin-statistics Theoremsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new derivation of the CPT and spin-statistics theorems in noncommutative field theories

Franco

Polito

2005

Journal of Mathematical Physics

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PCT, spin and statistics, and analytic wave front set

Soloviev

1999

Theor Math Phys

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A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined as generalized functions with test functions of compact support in momentum space. The vacuum expectation values are thereby admitted to be arbitrarily singular in their space-time dependence. The local commutativity condition is replaced by an asymptotic commutativity condition, which develops generalizations of the microcausality axiom previously proposed.

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On the Borchers class of a non-commutative field

Franco¹

2005

J. Phys. A: Math. Gen.

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In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asymptotic commutativity property, generalizing the notion of relative locality proved by Borchers in the framework of local QFT. We restrict ourselves to the simplest case of a scalar field theory with space-space non-commutativity.

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Extension of the spin-statistics theorem to nonlocal fields

Cited by 6 publications

References 4 publications

A new derivation of the CPT and spin-statistics theorems in noncommutative field theories

A new derivation of the CPT and spin-statistics theorems in noncommutative field theories

PCT, spin and statistics, and analytic wave front set

On the Borchers class of a non-commutative field

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