Semiclassical corrections to Kasner cosmologies

We consider the Einstein equations for a Bianchi type I geometry, modified by first-order semiclassical quantum corrections. Using reduction techniques developed by Parker and Simon, we simplify these equations, obtaining reduced forms containing only first and second derivatives. We then find analytical solutions for both the vacuum case and for the case of a perfect fluid with a stiff equation of state. In the vacuum case we find that the Kasner solution maintains the same form in both the classical and semiclassical regimes. In the matter-filled case we observe, however, that a qualitatively different behavior emerges in the semiclassical era. We comment on the nature of these differences.     

Planck-scale corrections to Friedmann equation

Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.     

Semiclassical solution to the BFKL equation with massive gluons

In this paper we proceed to study the high energy behavior of scattering amplitudes in a simple field model, with the Higgs mechanism for the gauge boson mass. The spectrum of the j-plane singularities of the t-channel partial waves and the corresponding eigenfunctions of the BFKL equation in leading \(\text {log}(1/x)\) approximation were previously calculated numerically. Here we develop a semiclassical approach to investigate the influence of the exponential decrease of the impact parameter dependence existing in this model, on the high energy asymptotic behavior of the scattering amplitude. This approach is much simpler than our earlier numerical calculations, and it reproduces those results. The analytical (semi-analytical) solutions which have been found in the approximation can be used to incorporate correctly the large impact parameter behavior in the framework of CGC/saturation approach. This behavior is interesting as it provides the high energy amplitude for the electroweak theory, which can be measured experimentally.     

Semiclassical kinetic equation and the WKB approximation

We study the connection between the classical response function of a nucleus described by the Vlasov equation and the corresponding quantum response function. In the limit of large quantum numbers, the Fourier coefficients which appear in the Vlasov theory correspond to the quantum matrix elements evaluated in the WKB approximation. The classical frequencies of motion give the quantum excitation energies according to the correspondence principle.For a central potential, we identify the normal modes of the classical systems with the corresponding shell-model transitions. Thus we can improve the Vlasov theory by excluding excitation modes which correspond to forbidden quantum transitions. Also, we study the effect of a spin-orbit force in the context of the Vlasov theory.Finally, always by exploiting the close analogy between the classical and the quantum response functions, we introduce exchange (Fock) term in the semiclassical RPA equation given by the Vlasov theory.     

Tree string generated corrections to Einstein gravity from the sigma model approach

We discuss the calculation of the three-loop-function for the twodimensional non-linear-model with torsion. It satisfies an integrability condition which leads to the ()^1,2-corrections (to Einstein gravity) generated from the theory of closed bosonic strings at the tree level. Some applications of these results are briefly discussed.     

Semiclassical spectral series for the two-component Hartree-type equation

Semiclassical spectral series for the two-component nonlinear Hartree-type operator corresponding to the rest point of the phase curve are constructed on the basis of the Maslov complex germ theory.     

Semiclassical approximation of the Dirac equation with supersymmetry

The general scheme of the successive construction of semiclassical approximation for the classical Dirac equation in a background Yang-Mills field, where the usual Dirac operator is replaced by that with supersymmetry, is suggested. The first two terms of the semiclassical expansion in Planck’s constant are derived in an explicit form. It is shown that supersymmetry of the initial Dirac operator leads to appearance of new additional terms in the classical equation of motion for spin of a particle and ipso facto requires appropriate modification for the Lagrangian of the spinning particle. The result obtained is used for the construction of one-to-one mapping between two Lagrangians of a classical color-charged spinning particle, one of which possesses local supersymmetry, and another doesn’t. It is demonstrated that for recovery of the one-to-oneness the additional terms obtained above in the semiclassical approximation of the Dirac operator with supersymmetry should be added to the Lagrangian without supersymmetry.     

Next-to-leading corrections to the BFKL equation from gluon and quark production

The gluon and quark production in the quasi-multi-Regge kinematics for the final particles is considered. The differential cross section for different helicity states is calculated. Dimensional regularization is used to remove the infrared divergencies in the corresponding contributions to the BFKL equation. The other next-to-leading corrections are discussed.     

Radiative corrections to the Dark Matter particles annihilation into massive leptons

We calculate the radiative corrections to the annihilation of the Dark Matter particles into leptons. Lepton masses are taken into account. For the Dark Matter particles we consider both Dirac and Majorana fermions. We sum up all the leading logarithmic contributions where it is possible. We investigate the mass dependence of the resulting cross sections and show that quantitatively the answer is very sensitive to the lepton mass due to the leading logarithm singularity.     

Nonlocal corrections to the Boltzmann equation for dense Fermi systems

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second-order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e. an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.     

On the Initial Conditions and Solutions of the Semiclassical Einstein Equations in a Cosmological Scenario

In this paper we shall discuss the backreaction of a massive quantum scalar field on the curvature, the latter treated as a classical field. Furthermore, we shall deal with this problem in the realm of cosmological spacetimes by analyzing the Einstein equations in a semiclassical fashion. More precisely, we shall show that, at least on small intervals of time, solutions for this interacting system exist. This result will be achieved providing an iteration scheme and showing that the series, obtained starting from the massless solution, converges in the appropriate Banach space. The quantum states with good ultraviolet behavior (Hadamard property), used in order to obtain the backreaction, will be completely determined by their form on the initial surface if chosen to be lightlike. Furthermore, on small intervals of time, they do not influence the behavior of the exact solution. On large intervals of time the situation is more complicated but, if the spacetime is expanding, we shall show that the end-point of the evolution does not depend strongly on the quantum state, because, in this limit, the expectation values of the matter fields responsible for the backreaction do not depend on the particular homogeneous Hadamard state at all. Finally, we shall comment on the interpretation of the semiclassical Einstein equations for this kind of problems. Although the fluctuations of the expectation values of pointlike fields diverge, if the spacetime and the quantum state have a large spatial symmetry and if we consider the smeared fields on regions of large spatial volume, they tend to vanish. Assuming this point of view the semiclassical Einstein equations become more reliable.     

Semiclassical quantization of the nonlinear Schrödinger equation

Using the functional integral technique of Dashen, Hasslacher, and Neveu, we perform a semiclassical quantization of the nonlinear Schrödinger equation, which reproduces McGuire's exact result for the energy levels of the theory's bound states. We show that the stability angle formalism leads to the one-loop normal ordering and self-energy renormalization expected from perturbation theory and demonstrate that taking into account center-of-mass motion gives the correct nonrelativistic energymomentum relation. We interpret the classical solution in the context of the quantum theory, relating it to the matrix element of the field operator between adjacent bound states in the limit of large quantum numbers. Finally, we quantize the NLSE as a theory of N component fermion fields and show that the semiclassical method yields the exact energy levels and correct degeneracies.