Statistics and UV-IR mixing with twisted Poincaré invariance

Balachandran, A. P.; Govindarajan, T. R.; Mangano, G.; Pinzul, A.; Qureshi, B. A.; Vaidya, Sachindeo

doi:10.1103/physrevd.75.045009

Cited by 116 publications

(201 citation statements)

References 9 publications

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“…The lack of locality leads to a failure of causality [30], and the spin-statistics theorem also fails to be valid. In particular, the Pauli exclusion principle is not expected to be valid for theories based on the algebra (31), and bounds on the deformation parameter a can be obtained from the bounds on the validity of the Pauli exclusion principle [22,23].…”

Section: Twisted Statistics In κ Spacementioning

confidence: 99%

“…This issue has naturally arisen in the context of noncommutative quantum mechanics and field theory [20,21,22,23,24]. In the noncommutative case, the issue of statistics is closely related to the symmetry of the noncommutative spacetime on which the dynamics is being studied.…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of noncommutativity, it is thus natural to demand that the statistics is invariant under the action of the twisted symmetry. This condition leads to a new twisted flip operator, which is compatible with the twisted coproduct of the symmetry group [22,23]. The operators projecting to the symmetric and antisymmetric sectors of the Hilbert space are then constructed from the twisted flip operator.…”

Section: Introductionmentioning

confidence: 99%

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Twisted statistics inκ-Minkowski spacetime

et al. 2008

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We consider the issue of statistics for identical particles or fields in κ-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription. I. INTRODUCTIONNoncommutative geometry is a plausible candidate for describing physics at the Planck scale, a simple model of which is given by the Moyal plane [1]. The models of noncommutative spacetime that follow from combining general relativity and uncertainty principle can be much more general [2]. An example of this more general class is provided by the κ-deformed space [3,4,5], which is based on a Lie algebra type noncommutativity. Apart from its algebraic aspects [6,7,8,9,10,11], various features of field theories and symmetries on κ-deformed spaces have recently been studied [12,13,14,15,16]. Such a space has also been discussed in the context of doubly special relativity [17,18,19].The issue of particle statistics plays a central role in the quantum description of a many-body system or field theory. This issue has naturally arisen in the context of noncommutative quantum mechanics and field theory [20,21,22,23,24]. In the noncommutative case, the issue of statistics is closely related to the symmetry of the noncommutative spacetime on which the dynamics is being studied. If a symmetry acts on a noncommutative spacetime, its coproduct usually has to be twisted in order to make the symmetry action compatible with the algebraic structure. In the commutative case, particle statistics is superselected, i.e. it is preserved under the action of the symmetry. In the presence of noncommutativity, it is thus natural to demand that the statistics is invariant under the action of the twisted symmetry. This condition leads to a new twisted flip operator, which is compatible with the twisted coproduct of the symmetry group [22,23]. The operators projecting to the symmetric and antisymmetric sectors of the Hilbert space are then constructed from the twisted flip operator. While most of the discussion of statistics in the noncommutative setup has been done in the context of the Moyal plane, some related ideas for κ-deformed spaces have also appeared recently [25,26,27].In this paper we set up a general formalism to describe statistics in κ-deformed spaces. Our formalism presented here is applicable to a system with an arbitrary symmetry group, which may include Poincare, Lorentz, Euclidean * trg@imsc.res.in † kumars.gupta@saha.ac.in ‡ harisp@uohyd.ernet.in § meljanac@irb.hr ¶ dmeljan@irb.hr

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Section: Twisted Statistics In κ Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Twisted statistics inκ-Minkowski spacetime

et al. 2008

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“…Твистованная CCR-алгебра (21) обсуждалась с разных точек зрения в работах [6], [19]- [22]. Как уже было сказано, эта деформация сохраняет трансляционную инва-риантность, но она очевидным образом нарушает лоренц-инвариантность.…”

Section: тождество (16) вытекает непосредственно из определения (15)unclassified

Некоммутативные Деформации Квантовых Теорий Поля, Локальность И Причинность

Соловьев¹,

Soloviev²

2010

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Исследуются некоммутативные деформации квантовых теорий поля для раз-личных звездочных произведений. Особое внимание уделяется локальным свой-ствам и регулярности деформированных полей. С использованием методов функционального анализа описаны основные структурные свойства вакуум-ных средних звездочно модифицированных произведений полей и полевых ком-мутаторов. В качестве замены условия микропричинности введено понятие θ-локальности, где θ -параметр некоммутативности. Проанализированы усло-вия сходимости и непрерывности звездочных произведений и определена алгеб-ра функций, наиболее адекватная произведениям Мойала и Вика-Вороса. Эта алгебра соответствует концепции строгого деформационного квантования и яв-ляется полезным средством при построении квантовой теории поля на неком-мутативном пространстве-времени.Ключевые слова: некоммутативная квантовая теория поля, звездочные произведения Мойала и Вика-Вороса, локальность, причинность, топологическая алгебра целых функ-ций. ВВЕДЕНИЕИнтенсивное исследование моделей некоммутативной теории поля в последние годы мотивировано фундаментальными проблемами квантовой физики и теории гравитации [1]. Хотя идея некоммутативности пространства-времени достаточно стара и, как хорошо известно, восходит к Гейзенбергу и Снайдеру, развитие тео-рии струн вызвало новую волну интереса к этой области исследований (см., напри-мер, обзор [2]). Почти все работы по этой тематике исходят из замены обычно-го поточечного произведения функций на пространстве-времени некоммутативным звездочным произведением. Как следствие, координатные функции удовлетворяют коммутационному соотношениюгде θ µν -вещественная антисимметричная матрица, играющая роль параметра не-коммутативности и определяющая деформацию пространства Минковского. Одна- * Физический институт им. П. Н. Лебедева РАН, Москва, Россия.

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“…2. Even free twisted noncommutative field theory is non-local, because one has q|[φ (x), φ (y)]|p = 0 for q = p and space-like separations [35].…”

Section: Twisted Noncommutative Quantum Field Theorymentioning

confidence: 99%