Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

We consider noncommutative gauge theory defined by means of Seiberg–Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg–Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang–Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.     

Inflation mechanism in asymptotic noncommutative geometry

The possibility of having an inflationary epoch within a noncommutative geometry approach to unifying gravity and the Standard Model is demonstrated. This inflationary phase occurs without the need to introduce ad hoc additional fields or potentials, rather it is a consequence of a nonminimal coupling between the geometry and the Higgs field.     

Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

Axion-like particles,cosmic magnetic fields and gamma-ray astrophysics

Axion-like particles (ALPs) are predicted by many extensions of the Standard Model and give rise to characteristic dimming and polarization effects in a light beam travelling in a magnetic field. In this Letter, we demonstrate that photon-ALP mixing in cosmic magnetic fields produces an observable distortion in the energy spectra of distant gamma-ray sources (like AGN) for ranges of the ALP parameters allowed by all available constraints. The resulting effect is expected to show up in the energy band 100 MeV–100 GeV, and so it can be searched with the upcoming GLAST mission.     

Perturbed nonlinear models from noncommutativity

Some discrete two-dimensional many particle systems are investigated inside the context of a deformed Newtonian mechanics obtained as a classical limit of a noncommutative quantum mechanics where the noncommutativity includes all degrees of freedom of the theory. Also, applying the continuous limit some alternative noncommutative generalizations of two-dimensional field theories have been constructed.     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.     

Technical remarks and comments on the UV/IR-mixing problem of a noncommutative scalar quantum field theory

The possibility of a resummation procedure in order to cure the UV/IR-mixing problem of noncommutative field theories is discussed. The method is presented for a scalar φ⁴ theory on Euclidean space. Finally, we sketch the idea of resummation forU(1)-gauge theories.     

Real-time gauge theory simulations from stochastic quantization with optimized updating

We investigate simulations for gauge theories on a Minkowskian space–time lattice. We employ stochastic quantization with optimized updating using stochastic reweighting or gauge fixing, respectively. These procedures do not affect the underlying theory but strongly improve the stability properties of the stochastic dynamics, such that simulations on larger real-time lattices can be performed.     

An anthology of non-local QFT and QFT on non-commutative spacetime

Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject.     

Quantum Hall effect in noncommutative quantum mechanics

We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.     

Cosmic microwave background fluctuations from gravitational waves: An analytic approach

We develop an analytic approach to calculation of the temperature and polarisation power spectra of the cosmic microwave background due to inflationary gravitational waves. This approach complements the more precise numerical results by providing insight into the physical origins of the features in the power spectra. We explore the use of analytic approximations for the gravitational-wave evolution, making use of the WKB approach to handle the radiation-matter transition. In the process, we describe scaling relations for the temperature and polarisation power spectra. We illustrate the dependence of the amplitude, shape, and peak locations on the details of recombination, the gravitational-wave power spectrum, and the cosmological parameters, and explain the origin of the peak locations in the temperature and polarisation power spectra. The decline in power on small scales in the polarisation power spectra is discussed in terms of phase-damping. In an appendix we detail numerical techniques for integrating the gravitational-wave evolution in the presence of anisotropic stress from free-streaming neutrinos.     

Noncommutative Wess–Zumino–Witten actions and their Seiberg–Witten invariance

We analyze the noncommutative two-dimensional Wess–Zumino–Witten model and its properties under Seiberg–Witten transformations in the operator formulation. We prove that the model is invariant under such transformations even for the noncritical (non-chiral) case, in which the coefficients of the kinetic and Wess–Zumino terms are not related. The pure Wess–Zumino term represents a singular case in which this transformation fails to reach a commutative limit. We also discuss potential implications of this result for bosonization.     

Lattice gauge fields and noncommutative geometry

Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified space-time or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lott are then used to develop gauge theories on this algebra and to derive Wilson's actions for the gauge and Dirac fields therefrom which can now be given geometrical meaning. We also describe very natural candidates for the QCD θ-term and Chern-Simons action suggested by this algebraic formulation. Some of these formulations are simpler than currently available alternatives. The paper treats both the functional integral and Hamiltonian approaches.     

Vanishing β-function for Grosse–Wulkenhaar model in a magnetic field

We prove that the β-function of the Grosse–Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared fixed point. Some consequences of these results are discussed.     

Gauge theory of the star product

The choice of a star product realization for non-commutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for non-commutative theories.     

Van der Waals interactions and Photoelectric Effect in Noncommutative Quantum Mechanics

We calculate the long-range Van der Waals force and the photoelectric cross section in a noncommutative setup. It is argued that non-commutativity effects could not be discerned for the Van der Waals interactions. The result for the photoelectric effect shows deviation from the usual commutative one, which in principle can be used to put bounds on the space-space non-commutativity parameter.     

Remarks on Exactly Solvable Noncommutative Quantum Field

We study exactly the solvable noncommutative scalar quantum field models of （2n） or （2n ＋ 1） dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B. 0 = 4-1 in field theoretic context means the full restoration of the maximal U（∞） gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1＋1-dimensional Moyal/matrix-valued nonlinear Schr6dinger （MNLS） equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.     

Effect of Temperature on Polaron Stability in a One-Dimensional Organic Lattice

Effect of temperature on the polaron stability in a one-dimensional organic lattice is investigated within the Su-Schrieffer-Heeger model. The temperature effect is simulated by introducing random forces to the equation of the lattice motion. It is found that the localized polaron state becomes delocalized even at low temperatures. The time of polaron keeping localized depends on the magnitude of temperatures. By taking into account the thermal effect, we find that the dissociation field is weaker as compared with earlier works.