arXiv subjects

A. Tureanu

Publications and source records attributed to A. Tureanu.

At least 55 records · Page 3Linked to original sources

arXiv2007

Noncommutative fields and actions of twisted Poincare algebra

Within the context of the twisted Poincaré algebra, there exists no noncommutative analogue of the Minkowski space interpreted as the homogeneous space of the Poincaré group quotiented by the Lorentz group. The usual definition of commutative classical fields as sections of associated vector bundles on the homogeneous space does not generalise to the noncommutative setting, and the twisted Poincaré algebra does not act on noncommutative fields in a canonical way. We make a tentative proposal for the definition of noncommutative classical fields of any spin over the Moyal space, which has the desired representation theoretical properties. We also suggest a way to search for noncommutative Minkowski spaces suitable for studying noncommutative field theory with deformed Poincaré symmetries.

hep-th↗

arXiv2007

Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity

A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters $Θ^{μν}$. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of General Relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.

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arXiv2007

Gauge-Dependence of Green's Functions in QCD and QED

When all Green's functions are known in a given gauge we may raise a question of whether it is possible or not to derive the corresponding ones in a different gauge. The answer is negative in QCD but affirmative in QED provided that we confine ourselves to the covariant gauge characterized by a gauge parameter $α$. We shall discuss the physical significance of this conclusion.

hep-th↗

arXiv2007

Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation

Based on the analysis of the most natural and general ansatz, we conclude that the concept of twist symmetry, originally obtained for the noncommutative space-time, cannot be extended to include internal gauge symmetry. The case is reminiscent of the Coleman-Mandula theorem. Invoking the supersymmetry may reverse the situation.

hep-th↗

arXiv2006

Generalized Haag's Theorem in SO(1,1) and SO(1,3) Invariant Quantum Field Theory

One of the most important results of the axiomatic quantum field theory - generalized Haag's theorem - is proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained: it has been proved that equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and total cross-sections in these theories.

hep-th↗

arXiv2006

Classical Theorems in Noncommutative Quantum Field Theory

Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.

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arXiv2006

Twist Symmetry and Gauge Invariance

By applying properly the concept of twist symmetry to the gauge invariant theories, we arrive at the conclusion that previously proposed in the literature noncommutative gauge theories, with the use of $\star$-product, are the correct ones, which possess the twisted Poincaré symmetry. At the same time, a recent approach to twisted gauge transformations is in contradiction with the very concept of gauge fields arising as a consequence of {\it local} internal symmetry. Detailed explanations of this fact as well as the origin of the discrepancy between the two approaches are presented.

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arXiv2005

Noncommutativity of Space and Rotation of Polarization of Light in a Background Magnetic Field

Recently the PVLAS collaboration has reported the observation of rotation of polarization of light propagating in a background magnetic field. In this letter we explore the possibility that such a rotation is a result of noncommutativity in the background space-time. To explain the reported polarization rotation within noncommutative QED we need the noncommutativity parameter $θ\simeq (30 {\rm GeV})^{-2}$.

hep-ph↗

arXiv2005

An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift

Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.

hep-th↗

arXiv2004

Jost-Lehmann-Dyson Representation and Froissart-Martin Bound in Quantum Field Theory on Noncommutative Space-Time

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with $SO(1,1)\times SO(2)$ symmetry, which is the feature arising when one has only space-space noncommutativity ($θ_{0i}=0$), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition usually taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the $2\to 2$-scattering amplitude in $\cosΘ$, $Θ$ being the scattering angle. A physical choice of the causality condition rescues the situation and as a result an analog of Lehmann's ellipse as domain of analyticity in $\cosΘ$ is obtained. However, the enlargement of this analyticity domain to Martin's ellipse and the derivation of the Froissart bound for the total cross-section in NC QFT is possible {\it only} in the special case when the incoming momentum is orthogonal to the NC plane. This is the first example of a nonlocal theory in which the cross-sections are subject to a high-energy bound. For the general configuration of the direction of the incoming particle, although the scattering amplitude is still analytic in the Lehmann ellipse, no bound on the total cross-section has been derived. This is due to the lack of a simple unitarity constraint on the partial-wave amplitudes, which could be used in this case. High-energy upper bounds on the total cross-section, among others, are also obtained for an arbitrary flat (noncompact) dimension of NC space-time.

hep-th↗

arXiv2004

New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications

We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincaré symmetry (with all 10 generators), as proposed in ref. [7]. This allows to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincaré symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag's theorem.

hep-th↗

arXiv2004

On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT

By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_μ,x_ν]=iθ_{μν}$, where $θ_{μν}$ is a {\it constant} real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré symmetry on QFT on such a space-time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincaré symmetry.

hep-th↗

arXiv2003

Noncommutative Standard Model: Model Building

A noncommutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: 1) although we can have noncommutative U(n) (which we denote by $U_{\star}(n)$) gauge theory we cannot have noncommutative SU(n) and 2) the charges in noncommutative QED are quantized to just $0, \pm 1$. We show how the problem with charge quantization, as well as with the gauge group, can be resolved by taking $U_{\star}(3)\times U_{\star}(2)\times U_{\star}(1)$ gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the noncommutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the noncommutative Standard Model (NCSM). In addition, among several peculiar features of our model, we address the {\it inherent} CP violation and new neutrino interactions.

hep-th↗

arXiv2003

Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory

We derive the analytical properties of the elastic forward scattering amplitude of two scalar particles from the axioms of the noncommutative quantum field theory. For the case of only space-space noncommutativity, i.e. $θ_{0i}=0$, we prove the dispersion relation which is similar to the one in commutative quantum field theory. The proof in this case is based on the existence of the analog of the usual microcausality condition and uses the Lehmann-Symanzik-Zimmermann (LSZ) or equivalently the Bogoliubov-Medvedev-Polivanov (BMP) reduction formalisms. The existence of the latter formalisms is also shown. We remark on the general noncommutative case, $θ_{0i}\neq0$, as well as on the nonforward scattering amplitude and mention their peculiarities.

hep-th↗

arXiv2003

Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory

The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.

hep-th↗

arXiv2002

Comments on the Hydrogen Atom Spectrum in the Noncommutative Space

There has been disagreement in the literature on whether the hydrogen atom spectrum receives any tree-level correction due to noncommutativity. Here we shall clarify the issue and show that indeed a general argument on the structure of proton as a nonelementary particle leads to the appearance of such corrections. As a showcase, we evaluate the corrections in a simple nonrelativistic quark model with a result in agreement with the previous one we had obtained by considering the electron moving in the external electric field of proton. Thus the previously obtained bound on the noncommutativity parameter, $θ< (10^4 GeV)^{-2}$, using the Lamb shift data, remains valid.

hep-th↗

arXiv2002

Spin-Statistics and CPT Theorems in Noncommutative Field Theory

We show that Pauli's spin-statistics relation remains valid in noncommutative quantum field theories (NC QFT), with the exception of some peculiar cases of noncommutativity between space and time. We also prove that, while the individual symmetries C and T, and in some cases also P, are broken, the CPT theorem still holds in general for noncommutative field theories, in spite of the inherent nonlocality and violation of Lorentz invariance.

hep-th↗

arXiv2001

Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects

After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with non-trivial topology and the operator representation of the $\star$-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed.

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