A Mermin–Wagner Theorem for Gibbs States on Lorentzian Triangulations

We establish a Mermin–Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution P of a critical Galton–Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus M of dimension d, with a given group action of a torus G of dimension d′≤d. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential U(x,y) invariant under the action of G. We analyze quenched Gibbs measures generated by U and prove that, for P-almost all Lorentzian triangulations, every such Gibbs measure is G-invariant, which means the absence of spontaneous continuous symmetry-breaking.     

Smooth Crossed Products of Rieffel’s Deformations

Assume ${\mathcal{A}}$ is a Fréchet algebra equipped with a smooth isometric action of a vector group V, and consider Rieffel’s deformation ${\mathcal{A}_J}$ of ${\mathcal{A}}$ . We construct an explicit isomorphism between the smooth crossed products ${V\ltimes\mathcal{A}_J}$ and ${V\ltimes\mathcal{A}}$ . When combined with the Elliott–Natsume–Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the case of smooth subalgebras of C^*-algebras, we also get a simple proof of equivalence of Rieffel’s and Kasprzak’s approaches to deformation.     

Towards Lax Formulation of Integrable Hierarchies of Topological Type

To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider the Hirota and Lax formulations of the deformation of the hierarchy of N copies of KdV obtained by an infinitesimal action of the Givental group. By first deforming the Hirota quadratic equations and then applying a fundamental lemma to express it in terms of pseudo-differential operators, we show that such deformed hierarchy admits an explicit Lax formulation. We then compare the deformed Hamiltonians obtained from the Lax equations with the analogous formulas obtained in Buryak et al. (J Differ Geom 92:153–185, 2012), Buryak et al. (J Geom Phys 62:1639–1651, 2012) to find that they agree. We finally comment on the possibility of extending the Hirota and Lax formulation on the whole orbit of the Givental group action.     

Classical {\mathcal{W}}-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents

We derive explicit formulas for λ-brackets of the affine classical \({\mathcal{W}}\) -algebras attached to the minimal and short nilpotent elements of any simple Lie algebra \({\mathfrak{g}}\) . This is used to compute explicitly the first non-trivial PDE of the corresponding integrable generalized Drinfeld–Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov’s equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h ˇ?3 functions, where h ˇ is the dual Coxeter number of \(\mathfrak{g}\) . In the case when \(\mathfrak{g}\) is \({\mathfrak{sl}_2}\) both these equations coincide with the KdV equation. In the case when \(\mathfrak{g}\) is not of type \({C_n}\) , we associate to the minimal nilpotent element of \(\mathfrak{g}\) yet another generalized Drinfeld–Sokolov hierarchy.     

Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables

It is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products $$\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n $$ ofWightman orJaffe fields.     

$$\mathrm{SL}(2, \mathbb {C})$$ group action on cohomological field theories

We introduce the \(\mathrm {SL} (2,\mathbb {C})\) group action on a partition function of a cohomological field theory via a certain Givental’s action. Restricted to the small phase space we describe the action via the explicit formulae on a CohFT genus g potential. We prove that applied to the total ancestor potential of a simple-elliptic singularity the action introduced coincides with the transformation of Milanov–Ruan changing the primitive form (cf. Milanov and Ruan in Gromov–Witten theory of elliptic orbifold \(\mathbb {P}^{1}\) and quasi-modular forms, arXiv:1106.2321, 2011).     

Semi-Classical Twists for {\mathfrak{sl}}_{3} and {\mathfrak{sl}}_{4} Boundary r-Matrices of Cremmer–Gervais Type

We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of $U({\mathfrak{sl}}_{3})$ and $U({\mathfrak{sl}}_{4})$ . In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer–Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in ${\mathfrak{sl}}_{n}$ .     

Rigorous information-theoretic derivation of quantum-statistical thermodynamics. II

Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state. The general formula developed there for the best-guess density operator \(\hat \rho\) was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumD _H of strong equilibrium density operators. In Part II mathematical evaluation of \(\hat \rho\) is completed after an epistemological analysis which leads first to the discretization ofD _H and then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions. Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized.     

Classical {\mathcal{W}} -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras

We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical ${\mathcal{W}}$ W -algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.     

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4?2ε dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop ε-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.     

A fast, low perturbation ionization beam profile monitor based on a gas-jet curtain for the ultra low energy storage ring

An ionization beam profile monitor relying on a supersonic gas-jet shaped into an extended, thin curtain is proposed for operation in an ultra high vacuum environment for very low perturbation on the accelerated beam, as requested for the in-ring profile monitoring at the Ultra low energy Storage Ring (USR) at the Facility for Low-energy Antiproton and Ion Research (FLAIR), in Darmstadt. In this paper, we describe the working principle of the monitor, as well as providing an analysis of sensitivity and resolution dependence on geometrical design and gas curtain thickness.     

Magnetic hyperfine field at Cr site in AgCrO2 given by Perturbed angular correlations

This work presents an electric field gradient and magnetic hyperfine field study, in the AgCrO₂ multiferroic with triangular spin lattice. The temperature dependence of the electric field gradient (efg) and magnetic hyperfine field (mhf) at Cr site was studied at isolde via perturbed angular correlation measurements with the ¹¹¹In probe, at room temperature and below the Néel temperature (T?≤?21 K) down to 12 K. The results show the presence of two distinct local environments. One axial symmetric efg with a very low mhf, and a non axially symmetric efg with a much higher one. The temperature dependences of mhf magnitude and of the angle between the mhf and the principle component of the efg are investigated.     

Simulating spin-\frac{3}{2} particles at colliders

Support for interactions of spin- $\frac{3}{2}$ particles is implemented in the FeynRules and ALOHA packages and tested with the MadGraph 5 and CalcHEP event generators in the context of three phenomenological applications. In the first, we implement a spin- $\frac{3}{2}$ Majorana gravitino field, as in local supersymmetric models, and study gravitino and gluino pair-production. In the second, a spin- $\frac{3}{2}$ Dirac top-quark excitation, inspired from compositeness models, is implemented. We then investigate both top-quark excitation and top-quark pair-production. In the third, a general effective operator for a spin- $\frac{3}{2}$ Dirac quark excitation is implemented, followed by a calculation of the angular distribution of the s-channel production mechanism.     

Heat Trace and Spectral Action on the Standard Podleś Sphere

We give a new definition of dimension spectrum for non-regular spectral triples and compute the exact (i.e., not only the asymptotics) heat-trace of standard Podle? spheres \({S^2_q}\) for 0 < q < 1, study its behaviour when \({q\to 1}\) , and fully compute its exact spectral action for an explicit class of cut-off functions.     

Preliminary design studies of an extraction of the USR

The next-generation Facility for Low energy Antiproton and Ion Research (FLAIR) at GSI is going to be a dedicated research facility for ion research in the keV range. These ion beams will allow to explore fundamental properties in matter-antimatter research at ultra-low energies of only 20 keV/q in hitherto impossible experiments. To provide these very low energy beams, the Ultra-low energy Storage Ring (USR), an electrostatic synchrotron, will play a major role within the FLAIR complex. It combines the electrostatic storage mode with deceleration from an initial energy of 300 keV/q down to 20 keV/q—as well as an efficient beam cooling. To fulfill its role as a multi-purpose experimental facility, the design of the USR has not only to cover in-ring experiments, but needs to include a highly flexible beam extraction for serving different external experiments as well.     

Synthesis and anti-cancer activity of a glycosyl library of \varvec{N}-acetylglucosamine-bearing oleanolic acid

N-Acetylglucosamine-bearing triterpenoid saponins (GNTS) were reported to be a unique type of saponins with potent anti-tumor activity. In order to study the structure–activity relationship of GNTS, 24 oleanolic acid saponins with ( $1 \rightarrow 3$ )-linked, ( $1\rightarrow 4$ )-linked, ( $1\rightarrow 6$ )-linked $N$ -acetylglucosamine oligosaccharide residues were synthesized in a combinatorial and concise method. The cytotoxicity of these compounds toward the leukemia cell line HL-60 and the colorectal cancer cell line HT-29 could not be improved. Half maximal inhibition below $10\,\upmu \hbox {M}$ was achieved in one single case. The study revealed that the activity decreased following the order of $3^{\prime }>4^{\prime }>6^{\prime }$ glycosyl modifications. GNTS that incorporated (d/l)-xylose and l-arabinose at positions $3^{\prime }$ and $4^{\prime }$ were more potent than those bearing other sugars.     

Electroweak radiative corrections to single top production

Fortran subroutines to calculate helicity amplitudes with massive spin-3/2 particles, such as massive gravitinos, which couple to the standard model and supersymmetric particles via the supercurrent, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external gravitinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the gauge invariance of the helicity amplitudes.     

Exact generalized Fokker-Planck equation for arbitrary dissipative and nondissipative quantum-systems

We start from a density matrix equation in its most general form. It comprises the action of external fields on the system, internal interactions, as well as the action of dissipative mechanisms (heat-baths or reservoirs), which may be Markoffian or non-Markoffian. We then define a distribution function of a type introduced previously byHaken, Risken, Weidlich for atoms. This distribution function,f, which is now formulated quite generally with aid of projection operators,P _ik , establishes a connection between theP _ik 's and classical variablesv _ik . By means off it is possible to exactly calculate all quantum mechanical expectation values by purec-number procedures. If the basic density matrix equation is Markoffian, it is even possible to calculate all time-ordered multitime averages byc-number procedures usingf, as had been demonstrated byHaken, Risken andWeidlich. In the present paper we derive in an explicit way an exactc-number partial differential equation forf. It contains derivatives of arbitrarily high order. In important classes of problems, it can be reduced to an ordinary FokkerPlanck equation, however. Our new equation has many applications, e.g. in the quantum theory of lasers, nonlinear quantum optics, spinresonance, and spin-wave-theory, as will be demonstrated in forthcoming papers. We wish to thank Prof. W.Weidlich and Dipl. Phys. H.Vollmer for several valuable discussions. In addition, H.Vollmer has kindly checked our calculations.