Related papers: Quantum variance for Eisenstein Series

Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…

A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be…

To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference…

The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are…

We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.

The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…

The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical…

Let X be a smooth projectibe curve over a finite field. We consider the Hall algebra H whose basis is formed by isomorphism classes of coherent sheaves on X and whose typical structure constant is the number of subsheaves in a given sheaf…

In this paper, we compute constant terms of Eisenstein series defined over a totally real field, at various cusps. In his paper published in 2003, M. Ohta computed the constant terms of Eisenstein series of weight two over the field of…

Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…

The relativistic quantum phase space (QPS) formalism extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, thereby providing a unified setting where the uncertainty principle and…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter…

We evaluate the smoothed first moment of central values of a family of qudratic Hecke $L$-functions in the Gaussian field using the method of double Dirichlet series. The asymptotic formula we obtain has an error term of size…

Let $h(-n)$ be the class number of the imaginary quadratic field with discriminant $-n$. We establish an asymtotic formula for correlations involving $h(-n)$ and $h(-n-l)$, over fundamental discriminants that avoid the congruence class…

For a banded link $L$ in a surface times a circle, the Witten-Reshetikhin-Turaev invariants are topological invariants depending on a sequence of complex $2p$-th roots of unity $(A_p)_{p\in 2\mathbb{N}}$. We show that there exists a…

We prove an asymptotic formula expressing the regularized fourth moment of all newform Eisenstein series of primitive nebentypus as a mean value of $L$-functions. This is an analogue of the recent work of Djankovi\'c and Khan in the…

We consider the possibility that the SU(2) isospin symmetry, exact in strong interactions but only approximate in nature, is in fact a quantum group. Using a doublet of q-quarks, we build the wavefuntions of pi-mesons, nucleons and Delta…

Based on Garland's work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms,…

We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…