16546446
On the problem of renormalizability in non‐commutative gauge field models – a critical review
AbstractWhen considering quantum ﬁeld theories on non-commutative spaces one inevitablyencounters the infamous UV/IR mixing problem. So far, only very few renormalizablemodels exist and all of them describe non-commutative scalar ﬁeld theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as ‘θ-deformedspace’ R 4θ . In this work we discuss some major obstacles of constructing a renormalizablenon-commutative gauge ﬁeld model and sketch some possible ways out. 1 Introduction Ever since the ﬁrst non-commutative quantum ﬁeld theory models were constructed, thegreatest obstacle has been the infamous so-called UV/IR mixing problem [1], where certaintypes of Feynman graphs, the non-planar graphs, exhibit new unrenormalizable IR singular-ities in exceptional momenta (see [2, 3, 4] for a review). The situation improved dramaticallywhen the ﬁrst renormalizable scalar non-commutative model, the Grosse-Wulkenhaar model,was put forward [5, 6, 7]. Later, a second renormalizable scalar non-commutative quantumﬁeld theory was presented by Gurau
18811875
Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi**4 Theory
In this paper we elaborate on the translation-invariant renormalizable 4 theory in 4-dimensional non-commu\-ta\-tive space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.
118634727
Loop calculations for the non-commutative U⋆(1) gauge field model with oscillator term
Motivated by the success of the non-commutative scalar Grosse–Wulkenhaar model, a non-commutative U⋆(1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.
17541769
A vector supersymmetry killing IR divergences in non-commutative gauge theories
This is a report on the joint work with Francois Gieres, Stefan Hohenegger, Olivier Piguet and Manfred Schweda. We consider a non-commutative U(1) gauge theory with an extension which was originally proposed by A. A. Slavnov [3, 4] in order to get rid of UV/IR mixing problems. Here we show, that the improved IR behaviour of this model is mainly due to the appearence of a linear vector supersymmetry.
16216330
A vector supersymmetry in noncommutative U(1) gauge theory with the Slavnov term
We consider noncommutative U(1) gauge theory with the additional term, involving a scalar field λ, introduced by Slavnov in order to cure the infrared problem. We show that this theory, with an appropriate space-like axial gauge-fixing, exhibits a linear vector supersymmetry similar to the one present in the 2-dimensional BF model. This vector supersymmetry implies that all loop corrections are independent of the λAA-vertex and thereby explains why Slavnov found a finite model for the same gauge-fixing.
14134311
Improved localization of a renormalizable non-commutative translation invariant U(1) gauge model
Motivated by the recent work of Vilar et al. (arXiv:0902.2956) we enhance our non-commutative translation invariant gauge model (Blaschke D. N. et al., arXiv:0901.1681) by introducing auxiliary fields and ghosts forming a BRST doublet structure. In this way localization of the problematic term can be achieved without the necessity for any additional degrees of freedom. The resulting theory is suspected to be renormalizable. A rigorous proof, however, has not been accomplished up to now.
119170221
How strange are compact star interiors
We discuss a Nambu–Jona–Lasinio (NJL)-type quantum field theoretical approach to the quark matter equation of state with color superconductivity and construct hybrid star models on this basis. It has recently been demonstrated that with increasing baryon density, the different quark flavors may occur sequentially, starting with down-quarks only, before the second light quark flavor and at highest densities the strange quark flavor also appears. We find that color superconducting phases are favorable over non-superconducting ones, which entails consequences for thermodynamic and transport properties of hybrid star matter. In particular, for NJL-type models no strange quark matter phases can occur in compact star interiors due to mechanical instability against gravitational collapse, unless a sufficiently strong flavor mixing as provided by the Kobayashi–Maskawa–'t Hooft determinant interaction is present in the model. We discuss observational data on mass–radius relationships of compact stars which can put constraints on the properties of the dense matter equation of state.
55221431
Debye mass and heavy quark potential in a PNJL quark plasma
We calculate the Debye mass for the screening of the heavy quark potential in a plasma of massless quarks coupled to the temporal gluon background governed by the Polyakov loop potential within the PNJL model in RPA approximation. We give a physical motivation for a recent phenomenological fit of lattice data by applying the calculated Debye mass with its suppression in the confined phase due to the Polyakov loop to a description of the temperature dependence of the singlet free energy for QCD with a heavy quark pair at infinite separation. We compare the result to lattice data.
118530597
WKB - type approximations in the theory of vacuum particle creation in strong fields
Within the theory of vacuum creation of an $e^{+}e^{-}$ - plasma in the strong electric fields acting in the focal spot of counter-propagating laser beams we compare predictions on the basis of different WKB-type approximations with results obtained in the framework of a strict kinetic approach. Such a comparison demonstrates a considerable divergence results. We analyse some reasoning for this observation and conclude that WKB-type approximations have an insufficient foundation for QED in strong nonstationary fields. The results obtained in this work on the basis of the kinetic approach are most optimistic for the observation of an $e^{+}e^{-}$ - plasma in the range of optical and x-ray laser facilities. We discuss also the influence of unphysical features of non-adiabatic field models on the reliability of predictions of the kinetic theory.
431673
Dynamical Schwinger effect and high-intensity lasers. Realising nonperturbative QED
AbstractWe consider the possibility of experimental verification of vacuum e+e- pair creation at the focus of two counter-propagating optical laser beams with intensities 1020–10$^{22}~{\rm W/cm}^2$, achievable with present-day petawatt lasers, and approaching the Schwinger limit: 10$^{29}~{\rm W/cm}^2$ to be reached at ELI.
Our approach is based on the collisionless kinetic equation for the evolution of the e+ and e- distribution functions governed by a non-Markovian source term for pair production.
As possible experimental signals of vacuum pair production we consider e+e- annihilation into γ-pairs and the refraction of a high-frequency probe laser beam by the produced e+e- plasma.
We discuss the dependence of the dynamical pair production process on laser wavelength, with special emphasis on applications in the X-ray domain (X-FEL), as well as the prospects for μ+μ- and π+π- pair creation at high-intensity lasers.
We investigate perspectives for using high-intensity lasers as “boosters” of ion beams in the few-GeV per nucleon range, which is relevant, e.g., to the exploration of the QCD phase transition in laboratory experiments.
55228960
A new quark-hadron hybrid equation of state for astrophysics - I. High-mass twin compact stars
Aims. We present a new microscopic hadron-quark hybrid equation of state model for astrophysical applications, from which compact hybrid star configurations are constructed. These are compo sed of a quark core and a hadronic shell with first-order phase transition at their interface. The resulting mass-radius relations ar e in accordance with the latest astrophysical constraints. Methods. The quark matter description is based on a QCD motivated chiral approach with higher-order quark interactions in the Dirac scalar and vector coupling channels. For hadronic matter we select a relativistic mean-field equation of state with dens ity-dependent couplings. Since the nucleons are treated in the quasi-part icle framework, an excluded volume correction has been included for the nuclear equation of state at suprasaturation density which takes into account the finite size of the nucleons. Results. These novel aspects, excluded volume in the hadronic phase and the higher-order repulsive interactions in the quark phase, lead to a strong first-order phase transition with large late nt heat, i.e. the energy-density jump at the phase transitio n, which fulfills a criterion for a disconnected third-family branch of compact stars in the mass-radius relationship. These twin stars appear at high masses (∼ 2 M⊙) being relevant for current observations of high-mass pulsars. Conclusions. This analysis offers a unique possibility by radius observations of compact stars to probe the QCD phase diagram at zero temperature and large chemical potential and even to support the existence of a critical point in the QCD phase diagram.