Related papers: Periodic orbits contribution to the 2-point correl…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…
We present a comprehensive semiclassical investigation of the three-dimensional Sinai billiard, addressing a few outstanding problems in "quantum chaos". We were mainly concerned with the accuracy of the semiclassical trace formula in two…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
We compute the two-loop Sudakov form factor in three-dimensional N=6 superconformal Chern-Simons theory, using generalised unitarity. As an intermediate step, we derive the non-planar part of the one-loop four-point amplitude in terms of…
Recently, \cite{Cao:2025hio} demonstrated the $2$-split for form factor under specific kinematic constraints. This factorization is analogous to that observed in scattering amplitudes. A key consequence of this structure is the presence of…
Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and…
We have calculated the decay $\tau \rightarrow \nu \pi(K) \gamma$. We present the photon energy spectrum, the meson-photon invariant mass spectrum and the integrated rate as a function of a photon energy cut or an invariant mass cut. Both…
The form factor $g_{\rho \pi}^{(S)}(Q^{2})$ of the strange vector current transition matrix element $<\rho| \bar{s}\gamma_\mus|\pi>$ is calculated within the chiral quark model. A strange vector current of the constituent $U$- and D-quarks…
We consider the scalar form factor in $\tau \to K\pi \nu_\tau$ decays. It receives contributions both from the scalar resonance $K_0^*(1430)$ and from the scalar projection of off-shell vector resonances. We construct a model for the…
A new resummation of the $S$-factor of a composite system of two relativistic spin-1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential is presented. The analysis is performed in the framework of a…
Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in…
$K_{\ell 3}$ and $\pi_{e 3}$ transition form factors are calculated as an application of Dyson-Schwinger equations. The role of nonanalytic contributions to the quark--W-boson vertex is elucidated. A one-parameter model for this vertex…
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…
Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…
We study periodic wind-tree models, billiards in the plane endowed with $\mathbb{Z}^2$-periodically located identical connected symmetric right-angled obstacles. We exhibit effective asymptotic formulas for the number of (isotopy classes…
This paper illustrates the application of Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main…