International Journal of Modern Physics A

The random matrix model approach to quantum chromodynamics (QCD) with nonvanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral perturbation theory (∊χPT). Two types of matrix model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with ∊χPT. All known analytic results for the spectrum of complex and symplectic matrix models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent lattice simulations are also discussed.

Here, dark energy is obtained using dual roles of the Ricci scalar (as a physical field as well as geometry). Dark energy density, obtained in this model, mimics phantom and the derived Friedmann equation contains a term with ρ_de being the dark energy density and λ, called as cosmic tension. It is like brane-gravity inspired Friedmann equation, which arises here without using the brane-gravity theory. It is found that acceleration is a transient phenomenon for λ< 0, but for λ> 0 accelerated expansion is found to encounter the big-rip problem. It is shown that this problem can be avoided if the dark energy behaves as barotropic fluid and generalized Chaplygin gas simultaneously. Moreover, time for transition (from deceleration to acceleration of the universe) is derived as a function of equation of state parameter w_de = p_de/ρ_de with p_de being the pressure for dark energy fluid.

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four-dimensional (4D) Taub-NUT space–times. It is outlined a new geometric technique of constructing Ricci flow solutions. Some conceptual issues on space–times provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Einstein and Ricci flow equations.

A mechanism is discussed to obtain light scalar fields from a spontaneously broken continuous symmetry without explicitly breaking it. If there is a continuous manifold of classical vacua in orbit space, its tangent directions describe classically massless fields that may acquire mass from perturbations of the potential that do not break the symmetry. We consider the simplest possible example, involving a scalar field in the adjoint representation of SU(N). We study the scalar mass spectrum and its renormalization group running at one-loop level including scalar and pseudoscalar Yukawa couplings to a massive Dirac fermion.

We present a new procedure for quantizing field theory models on a noncommutative space–time. Our new quantization scheme depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by this quantization yields exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after the quantization. This implies, for instance, that the noncommutativity may be incorporated in the process of quantization, rather than in the action as conventionally done.

The possible application of boosted neural network to particle classification in high energy physics is discussed. A two-dimensional toy model, where the boundary between signal and background is irregular but not overlapping, is constructed to show how boosting technique works with neural network. It is found that boosted neural network not only decreases the error rate of classification significantly but also increases the efficiency and signal–background ratio. Besides, boosted neural network can avoid the disadvantage aspects of single neural network design. The boosted neural network is also applied to the classification of quark- and gluon-jet samples from Monte Carlo e⁺e^- collisions, where the two samples show significant overlapping. The performance of boosting technique for the two different boundary cases — with and without overlapping is discussed.

We compute the one-loop polarization tensor Π for the on-shell, massless mode in a thermalized SU(2) Yang–Mills theory being in its deconfining phase. Postulating that , we discuss Π's effect on the low-momentum part of the black-body spectrum at temperatures ~2,…,4 T_CMB where T_CMB ~ 2.73 K. A table-top experiment is proposed to test the above postulate. As an application, we point out a possible connection with the stability of dilute, cold, and old innergalactic atomic hydrogen clouds. We also compute the two-loop correction to the pressure arising from the instantaneous massless mode in unitary-Coulomb gauge, which formerly was neglected, and present improved estimates for subdominant corrections.

The master equations in the Euclidean Schwarzschild–Tangherlini space–time of a small static perturbation are studied. For each harmonic mode on the sphere there are two solutions that behave differently at infinity. One solution goes like the power 2-l-n of the radial variable, the other solution goes like the power l. These solutions occur in power series.

The second main statement of the paper is that any eigentensor of the Lichnerowicz operator in a Euclidean Schwarzschild space–time with an eigenvalue different from zero is essentially singular at infinity. Possible applications of the stability of instantons are discussed.

We present the analysis of a small static perturbation of the Euclidean Schwarzschild–Tangherlini metric tensor. The higher order perturbations will appear later. We determine independently the static perturbations of the Schwarzschild quantum black hole in dimension 1+n≥4, where the system of equations is reduced to master equations — ordinary differential equations. The solutions are hypergeometric functions which in some cases can be reduced to polynomials.

In the same Schwarzschild background, we analyze static perturbations of the scalar mode and show that there does not exist any static perturbation that is regular everywhere outside the event horizon and is well-behaved at the spatial infinity. This confirms the uniqueness of the spherically symmetric static empty quantum black hole, within the perturbation framework.

Our strategy for treating the stability problem is also applicable to other symmetric quantum black holes with a nonzero cosmological constant.

We established a resummed formula for the effective potential of scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g³ order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g³ order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.