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72
Noncommutative deformations of Wightman quantum field theories
, 2008
"... Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its WeylWi ..."
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Cited by 27 (3 self)
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Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its WeylWigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedgeshaped regions, and may therefore be used to compute noncommutative corrections to twoparticle Smatrix elements.
On 'full' twisted Poincare' symmetry and QFT on MoyalWeyl spaces
 Phys. Rev. D
"... We explore some general consequences of a proper, full enforcement of the “twisted Poincaré ” covariance of Chaichian et al [14], Wess [52], Koch et al [35], Oeckl [43] upon manyparticle quantum mechanics and field quantization on a MoyalWeyl noncommutative space(time). This entails the associated ..."
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Cited by 25 (0 self)
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We explore some general consequences of a proper, full enforcement of the “twisted Poincaré ” covariance of Chaichian et al [14], Wess [52], Koch et al [35], Oeckl [43] upon manyparticle quantum mechanics and field quantization on a MoyalWeyl noncommutative space(time). This entails the associated braided tensor product with an involutive braiding (or ⋆tensor product in the parlance of Aschieri et al [3, 4]) prescription for any coordinates pair of x,y generating two different copies of the space(time); the associated nontrivial commutation relations between them imply that x − y is central and its Poincaré transformation properties remain undeformed. As a consequence, in QFT (even with spacetime noncommutativity) one can reproduce notions (like spacelike separation, time and normalordering, Wightman or Green’s functions, etc), impose constraints (Wightman axioms), and construct free or interacting theories which essentially coincide with the undeformed ones, since the only observable quantities involve coordinate differences. In other words, one may thus well realize QM and QFT’s where the effect of space(time) noncommutativity amounts to a practically unobservable common noncommutative translation of all reference frames.
Supersymmetry in noncommutative superspaces
 J. High Energy Phys
"... Non commutative superspaces can be introduced as the MoyalWeyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending o ..."
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Cited by 14 (1 self)
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Non commutative superspaces can be introduced as the MoyalWeyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending on the differential operators used to define the Poisson bracket. Some examples of deformed, 4 dimensional lagrangians are given. For extended superspace (N> 1), some new deformations can be defined, with no analogue in the N = 1 case. 1 1
Free qdeformed relativistic wave equations by representation theory
 Eur. Phys. J. C
"... In a representation theoretic approach a free qrelativistic wave equation must be such, that the space of solutions is an irreducible representation of the qPoincaré algebra. It is shown how this requirement uniquely determines the qwave equations. As examples, the qDirac equation (including qg ..."
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Cited by 11 (1 self)
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In a representation theoretic approach a free qrelativistic wave equation must be such, that the space of solutions is an irreducible representation of the qPoincaré algebra. It is shown how this requirement uniquely determines the qwave equations. As examples, the qDirac equation (including qgamma matrices which satisfy a qClifford algebra), the qWeyl equations, and the qMaxwell equations are computed explicitly. 1
Telltale traces of U(1) fields in noncommutative standard model extensions
, 2006
"... Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. In this paper, we study a general class of 4dimensional noncommutative m ..."
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Cited by 11 (0 self)
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Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. In this paper, we study a general class of 4dimensional noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N1)×U(N2)×...× U(Nm) coupled to matter fields transforming in the (anti)fundamental, bifundamental and adjoint representations. Noncommutativity is introduced using the WeylMoyal starproduct approach on a continuous spacetime. We pay particular attention to overall traceU(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. We show that, in general, these traceU(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the lowenergy effective theory. Making these effects unobservable in the class of models we consider would require pushing the constraint on the noncommutativity mass scale far beyond the Planck mass (MNC � 10 100 MP) and severely limits the phenomenological prospects of
Noncommutativity, extra dimensions, and power law running
 in the infrared,” JHEP 0601
, 2006
"... We investigate the running gauge couplings of U(N) noncommutative gauge theories with compact extra dimensions. Power law running of the traceU(1) gauge coupling in the ultraviolet is communicated to the infrared by ultraviolet/infrared mixing, whereas the SU(N) factors run exactly as in the commut ..."
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Cited by 10 (1 self)
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We investigate the running gauge couplings of U(N) noncommutative gauge theories with compact extra dimensions. Power law running of the traceU(1) gauge coupling in the ultraviolet is communicated to the infrared by ultraviolet/infrared mixing, whereas the SU(N) factors run exactly as in the commutative theory. This results in theories where the experimentally excluded traceU(1) factors decouple with a power law running of the Gauge theories on spaces with noncommuting coordinates, [x µ, x ν] = i θ µν, (1.1) are an interesting class of quantum field theories with intriguing and sometimes unexpected features. These noncommutative models can arise naturally as lowenergy effective
Star product algebras of test functions
 Theor. Math. Phys
, 2007
"... Abstract. We prove that the GelfandShilov spaces S β α are topological algebras under the Moyal ⋆product if and only if α ≥ β. These spaces of test functions can be used to construct a noncommutative quantum field theory. The star product depends continuously on the noncommutativity parameter in t ..."
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Cited by 10 (6 self)
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Abstract. We prove that the GelfandShilov spaces S β α are topological algebras under the Moyal ⋆product if and only if α ≥ β. These spaces of test functions can be used to construct a noncommutative quantum field theory. The star product depends continuously on the noncommutativity parameter in their topology. We also prove that the series expansion of the Moyal product is absolutely convergent in S β α if and only if β < 1/2. 1.
FIANTD/200801 Failure of microcausality in noncommutative field theories
, 802
"... We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ: (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x), O(y)] and prove that, in the c ..."
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Cited by 9 (5 self)
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We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ: (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x), O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points. 1.
Locality, Causality and Noncommutative Geometry
, 2008
"... We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is vio ..."
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Cited by 9 (2 self)
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We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative spacetime. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity. 1