International Journal of Modern Physics A

The brick-wall method put forward by 't Hooft has contributed a great deal to the understanding and calculating of the entropy of a black hole. However, there are some drawbacks in it such as little mass approximation, neglecting logarithm terms, and taking the term including L³ as a contribution of the vacuum surrounding the black hole. Moreover, the fundamental problem is why the entropy of scalar field or Dirac field surrounding a black hole is the entropy of the black hole itself. It is well known that the event horizon is the characteristic of a black hole. The entropy calculation of a black hole should be only related to its horizon. Due to this analysis, we improve the brick-wall model by taking that the entropy of a black hole is only contributed by a thin film near the event horizon. This improvement not only gives us a satisfied result, but also avoids the drawbacks in the original brick-wall method. It is found that there is an intrinsic relation between the event horizon and the entropy. We also calculate the entropy of Schwarzschild–de Sitter space–time via the improved method, which can hardly be resolved via the original model.

The direct CP asymmetry in the inclusive B → X_dγ and B → X_de⁺e^- decays is investigated in the two-Higgs doublet extension of the Standard Model (2HDM). The investigation is performed in the lowest nonvanishing order of the perturbation theory using the existing restrictions on the 2HDM parameters space. It is shown that the direct CP asymmetry in the B → X_dγ decay can deviate significantly from the Standard Model predictions. In the presence of only one source of CP violation (the CKM matrix weak phase) a_CP(B → X_dγ) can have the sign opposite to that in the SM. The new source of CP violation can make |a_CP(B → X_dγ)| arbitrary small (unlike the SM case) and hence unmeasurable. Quantitatively, the obtained results suffer from the uncertainty of the choice of renormalization scale. As for the B → X_de⁺e^- rate asymmetry, its renormalization scale dependence in the lowest nonvanishing order does not allow to conclude if this quantity is efficient for testing new physics beyond the Standard Model.

We derive and solve numerically self-consistent flow equations for a general O(N)-symmetric effective potential without any polynomial truncation. The flow equations combined with a sort of a heat-kernel regularization are approximated in next-to-leading order of the derivative expansion. We investigate the method at finite temperature and study the nature of the phase transition in detail. Several beta functions, the Wilson–Fisher fixed point in three dimensions for various N are analyzed and various critical exponents β, ν, δ and η are independently calculated in order to emphasize the reliability of this novel approach.

Following a suggestion by Vafa, we present a quantum-mechanical model for S duality symmetries observed in the quantum theories of fields, strings and branes. Our formalism may be understood as the topological limit of Berezin's metric quantization of the upper half-plane H, in that the metric dependence of Berezin's method has been removed. Being metric-free, our prescription makes no use of global quantum numbers. Quantum numbers arise only locally, after the choice of a local vacuum to expand around. Our approach may be regarded as a manifestly nonperturbative formulation of quantum mechanics, in that we take no classical phase space and no Poisson brackets as a starting point. Position and momentum operators satisfying the Heisenberg algebra are defined and their spectra are analysed. We provide an explicit construction of the Hilbert space of states. The latter carries no representation of SL(2,R), due to the lifting of the metric dependence. Instead, the reparametrization invariance of H under SL(2,R) induces a natural SL(2,R) action on the quantum-mechanical operators that implements S duality. We also link our approach with the equivalence principle of quantum mechanics recently formulated by Faraggi–Matone.

We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU(2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

We prove that, given a time-independent Lagrangian defined in the first tangent bundle of configuration space, every infinitesimal Noether symmetry that is defined in the n-tangent bundle and is not vanishing on-shell, can be written as a canonical symmetry in an enlarged phase space, up to constraints that vanish on-shell. The proof is performed by the implementation of a change of variables from the n-tangent bundle of the Lagrangian theory to an extension of the Hamiltonian formalism which is particularly suited for the case when the Lagrangian is singular. This result proves the assertion that any Noether symmetry can be canonically realized in an enlarged phase space. Then we work out the regular case as a particular application of this ideas and rederive the Noether identities in this framework. Finally we present an example to illustrate our results.

An observation of the autocorrelation of Wilson loops on lattice is presented, especially for the small separation in Markov chain. We give a possible explanation for such behavior. We also present the dependence of autocorrelation behavior on the chosen operators in this paper.

We obtain a complete set of one-loop RGE's for a set of combinations of neutrino parameters for the case of two-fold degenerate hierarchical three-neutrino models. The requirement of consistency of exact solutions to these RGE's with the two-fold degeneracy yields conditions which have previously been obtained perturbatively/numerically. These conditions, in the limit |U_eν3| = 0, are shown to lead to a strong cancellation in the matrix element of neutrinoless double beta decay.