Renormalizable Theory Research Articles

Exorcizing the Landau ghost in noncommutative quantum field theory

We show that the simplest noncommutative renormalizable field theory, the ø4 model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theory

On the effective action of noncommutative Yang-Mills theory

We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable Yang-Mills theory.

Analyzing WMAP Observation by Quantum Gravity

The angular power spectra of cosmic microwave background are analyzed under the light of the evolutional scenario of the universe based on the renormalizable quantum theory of gravity in four dimensions. The equation of evolution is solved numerically fixing the power law spectrum predicted by the conformal gravity for the initial condition. The equation requires to introduce a dynamical energy scale about 10^{17}GeV, where the inflationary space-time evolution makes a transition to the big-bang of the conventional Friedmann universe. The quality of fit to the three-year data of WMAP implies the possibility to understand the observation by quantum gravity.

Self-consistent theory of phonon renormalization and electron-phonon coupling near a two-dimensional Kohn singularity

We show that the usual expression for evaluating electron-phonon coupling and the phonon linewidth in two-dimensional metals with a cylindrical Fermi surface cannot be applied near the wave vector corresponding to the Kohn singularity. Instead, the Dyson equation for phonons has to be solved self-consistently. If a self-consistent procedure is properly followed, there is no divergency in either the coupling constant or the phonon linewidth near the offending wave vectors, in contrast to the standard expression.

On the asymptotic transition to complexity in quantum chromodynamics

Quantum chromodynamics (QCD) is a renormalizable gauge theory that successfully describes the fundamental interaction of quarks and gluons. The rich dynamical content of QCD is manifest, for example, in the spectroscopy of complex hadrons or the emergence of quark–gluon plasma. There is a fair amount of uncertainty regarding the behavior of perturbative QCD in the infrared and far ultraviolet regions. Our work explores these two domains of QCD using non-linear dynamics and complexity theory. We find that local bifurcations of the renormalization flow destabilize asymptotic freedom and induce a steady transition to chaos in the far ultraviolet limit. We also conjecture that, in the infrared region, dissipative non-linearity of the renormalization flow supplies a natural mechanism for confinement.

Master crossover behavior of parachor correlations for one-component fluids

The master asymptotic behavior of the usual parachor correlations, expressing surface tension sigma as a power law of the density difference rho(L)-rho(V) between coexisting liquid and vapor, is analyzed for a series of pure compounds close to their liquid-vapor critical point, using only four critical parameters (beta(c))-1 , alpha(c) , Z(c) , and Y(c) , for each fluid. This is accomplished by the scale dilatation method of the fluid variables where, in addition to the energy unit (beta(c))-1 and the length unit alpha(c) , the dimensionless numbers Z(c) and Y(c) are the characteristic scale factors of the ordering field along the critical isotherm and of the temperature field along the critical isochore, respectively. The scale dilatation method is then formally analogous to the basic system-dependent formulation of the renormalization theory. Accounting for the hyperscaling law delta-1/delta+1=eta-2/2d , we show that the Ising-like asymptotic value pi(a) of the parachor exponent is unequivocally linked to the critical exponents eta or delta by pi(a)/d-1=2/d-(2-eta)=delta+1/d (here d=3 is the space dimension). Such mixed hyperscaling laws combine either the exponent eta or the exponent delta , which characterizes bulk critical properties of d dimension along the critical isotherm or exactly at the critical point, with the parachor exponent pi(a) which characterizes interfacial properties of d-1 dimension in the nonhomogeneous domain. Then we show that the asymptotic (symmetric) power law [abstract; see text] is the two-dimensional critical equation of state of the liquid-gas interface between the two-phase system at constant total (critical) density rho(c) . This power law complements the asymptotic (antisymmetric) form [abstract; see text] of the three-dimensional critical equation of state for a fluid of density rho not equal to rho_(c) and pressure p not equal to p_(c) , maintained at constant (critical) temperature T=T_(c)} [mu_(rho)(mu_(rho,c)) is the specific (critical) chemical potential; p_(c) is the critical pressure; and T_(c) is the critical temperature]. We demonstrate the existence of the related universal amplitude combination [abstract; see text] = universal constant, constructed with the amplitudes D_(rho)(sigma) and D_(rho)(c) , separating then the respective contributions of each scale factor Y_(c) and Z_(c) , characteristic of each thermodynamic path, i.e., the critical isochore and the critical isotherm (or the critical point), respectively. The main consequences of these theoretical estimations are discussed in light of engineering applications and process simulations where parachor correlations constitute one of the most practical methods for estimating surface tension from density and capillary rise measurements.

Period‐doubling cascades and mode interactions in coupled systems

AbstractSuppose that an iterated map exhibits a period‐doubling cascade. If two such maps are coupled, then the synchronised state will exhibit the same period‐doubling cascade but there is also the additional possibility of symmetry‐breaking bifurcations to non‐synchronised states. By introducing a second parameter, a symmetry‐breaking bifurcation and a period‐doubling bifurcation can be made to occur at the same point, resulting in a mode interaction.As the second parameter is varied from the value at the mode interaction, a second symmetry‐breaking bifurcation may occur from the period 2 solutions, which will then be involved in another mode interaction at the next period‐doubling bifurcation point. In this way, a complete cascade of mode interactions can occur.A local analysis of such a mode interaction is considered. The global consequences together with a classification of different cases are then analysed. Renormalisation theory is used to determine the universal behaviour and parameter scalings of such a system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Pion form factor in the Kroll-Lee-Zumino model

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used to compute the one-loop vertex corrections to the tree-level, vector meson dominance pion form factor. These corrections, together with the known one-loop vacuum polarization contribution, lead to a substantial improvement over vector meson dominance. The resulting pion form factor in the spacelike region is in excellent agreement with data in the whole range of accessible momentum transfers. The timelike form factor, known to reproduce the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order O(g{sub {rho}}{sub {pi}}{sub {pi}}{sup 2})

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in nonequilibrium systems at the instance of directed percolation (DP), which has become the paradigm of nonequilibrium phase transitions into absorbing states, above, at, and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities LI(x;λ), with λ a generic coupling constant, such that the following expression ∂LI(x;λ)/∂λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.

Supersymmetric adjointSU(5)

Recently we have proposed a renormalizable grand unified theory, based on the SU(5) gauge symmetry, where the neutrino masses are generated through the type I and type III seesaw mechanisms. In this letter we study the supersymmetric version of this theory. As in the non-susy version it is possible to generate all fermion masses with the minimal number of Higgses, the theory predicts one massless neutrino and the leptogenesis mechanism can be realized. All contributions to the decay of the proton and the properties of neutralinos are discussed. This theory can be considered as the simplest renormalizable supersymmetric grand unified theory based on the SU(5) gauge symmetry since it has the minimal number of superfields and free parameters.

A Lie Theoretic Approach to Renormalization

Motivated by recent work of Connes and Marcolli, based on the Connes–Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our results rely both on the properties of the Dynkin idempotent, one of the fundamental Lie idempotents in the theory of free Lie algebras, and on properties of Hopf algebras encapsulated in the notion of associated descent algebras. Besides leading very directly to proofs of the main combinatorial aspects of the renormalization procedures, the new techniques give rise to an algebraic approach to the Galois theory of renormalization. In particular, they do not depend on the geometry underlying the case of dimensional regularization and the Riemann–Hilbert correspondence. This is illustrated with a discussion of the BPHZ renormalization scheme.

Renormalizable adjoint [formula omitted

We investigate the possibility to find the simplest renormalizable grand unified theory based on the SU(5) gauge symmetry. We find that it is possible to generate all fermion masses with only two Higgs bosons, 5H and 45H. In this context the neutrino masses are generated through the type III and type I seesaw mechanisms. The predictions coming from the unification of gauge couplings and the stability of the proton are discussed in detail. In this theory the leptogenesis mechanism can be realized through the out of equilibrium decays of the fermions in the adjoint representation.

On dilatation operator for a renormalizable theory

Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators in the theory. In the spirit of AdS/CFT correspondence, this operator is interpreted as the Hamiltonian of the dual theory. In the case of a field theory with non-abelian gauge symmetry the resulting system is a matrix model. The one-loop case is analyzed in details and it is shown that we reproduce known results from = 4 supersymmetric Yang-Mills theory.

Unusual Suppression of Low Energy Spin Excitations near Fermi Level inAFe4Sb12(A=Ca, Sr, and Ba) Probed by Sb-NQR

Sb nuclear quadrupole resonances (NQR) have been performed on the alkaline-earth filled skutterudite A Fe 4 Sb 12 ( A =Ca, Sr, and Ba) being close to ferromagnetic instabiity. No hyperfine splitting in NQR spectrum even at the lowest temperature (1.5 K) confirms an absence of uniform ferromagnetic order in these compounds. Above about T * ∼70 K, the nuclear spin–lattice relaxation rate divided by temperature, 1/ T 1 T , follows an empirical relationship 1/ T 1 T = a + b χ spin with respect to the Curie Weiss (CW) like T -dependence of the static spin susceptibility χ spin . The correlation between 1/ T 1 T and χ spin is consistent with the self-consistent renormalization (SCR) theory for the three-dimensional (3D) nearly ferromagnet despite the relatively large contribution of the first term not correlating to χ spin . However, below about T * , 1/ T 1 T exhibits a gap-like suppression with a gap magnitude of about 65 K. This unusual suppression of the low energy spin excitations is contrasting to the cas...

Noncommutative induced gauge theory

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang–Mills-type effective theory generated from the integration over the scalar field. We find that the gauge-invariant effective action involves, beyond the expected noncommutative version of the pure Yang–Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative ϕ4-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.

Local renormalizable gauge theories from nonlocal operators

The possibility that nonlocal operators might be added to the Yang–Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator Tr ∫ A μ 1 D 2 A μ is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.

Resummation of Mass Terms in Perturbative Massless Quantum Field Theory

The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form $-\frac{m^2}{2} \Phi^2$ to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.

Riccion Field from Higher-Dimensional Theory and Renormalization

Riccion ¯elds are obtained through spontaneous compacti¯cation of (4 +D)¡dimensional Kaluza-Klein type theory. It is found that multiplicatively renormalizable quantum theory free from non-unitarity problem can be obtained for Riccion ¯elds which manifest material aspect of Recci scalar. The renormal- ization group improved e®ective lagrangian for these ¯elds is also derived.

Master singular behavior for the Sugden factor of one-component fluids near their gas-liquid critical point

We present the master (i.e., unique) behavior of the squared capillary length-the so-called Sugden factor-as a function of the temperaturelike field along the critical isochore, asymptotically close to the gas-liquid critical point of about twenty (one-component) fluids. This master behavior is obtained using the scale dilatation of the relevant physical fields of the one-component fluids. The scale dilatation method introduces the fluid-dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the Ising-like universality class. The master behavior for the Sugden factor satisfies hyperscaling. It can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain, recently obtained from massive renormalization in field theory. In the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension, we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the Sugden factor, in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one-component fluid "subclass."