相关论文: Analytic Continuation of Spin foam Models

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross--section. The particular problems of the Regge model and the exponential form of…

We apply the soft-collinear effective theory (SCET) to deep inelastic scattering near the endpoint region. The forward scattering amplitude, and the structure functions are shown to factorize as a convolution of the Wilson coefficients, the…

We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show…

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition…

We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the…

For two-dimensional, immersed closed surfaces $f:\Sigma \to \R^n$, we study the curvature functionals $\mathcal{E}^p(f)$ and $\mathcal{W}^p(f)$ with integrands $(1+|A|^2)^{p/2}$ and $(1+|H|^2)^{p/2}$, respectively. Here $A$ is the second…

We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it…

Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zeta function $Z(s)$ for several disjoint strictly convex compact obstacles $K_i \subset \R^N, i = 1,..., \kappa_0,\: \ka_0 \geq 3,$ and let $R_{\chi}(z) = \chi…

We study the landscapes of multi-species spherical spin glasses. Our results determine the phase boundary for annealed trivialization of the number of critical points, and establish its equivalence with a quenched strong topological…

We prove an entropy formula for certain expansive actions of a countable discrete residually finite group $\Gamma $ by automorphisms of compact abelian groups in terms of Fuglede-Kadison determinants. This extends an earlier result proved…

Finite rank median spaces are a simultaneous generalisation of finite dimensional ${\rm CAT}(0)$ cube complexes and real trees. If $\Gamma$ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of…

The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the…

The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented.Two-loop calculations and subsequent Pad\'e-Borel…

Pulsed-gradient spin-echo (PGSE) MRI experiments probe molecular self-diffusion through spin phase accumulation under time-dependent magnetic field gradients. For diffusion confined to cylindrical surfaces, existing analytical signal models…

We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin…

We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two…

We show that formal eigenvalue equations of analytic one-frequency Schr\"od-inger operators admit intrinsic analytic $Sp(2k,\C)$ structures, where $k=k(E)$ is the T-acceleration in global theory. For trigonometric potentials those…

This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schr\"odinger equation for this generalized Kepler-Coulomb system can be separated in prolate spheroidal…

We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdi{\`e}re's use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup…

Fix an elliptic curve $E/\Q$, and assume the generalized Riemann hypothesis for the $L$-function $ L(E_D, s) $ for every quadratic twist $E_D$ of $E$ by $D\in\Z$. We combine Weil's explicit formula with techniques of Heath-Brown to derive…