Related papers: Unitary Evolution on a Discrete Phase Space
A non-perturbative canonical quantization of Gowdy $T^3$ polarized models carried out recently is considered. This approach profits from the equivalence between the symmetry reduced model and 2+1 gravity coupled to a massless real scalar…
It is shown that time-harmonic hypersurface motions in various, conformally flat, N-dimensional manifolds admit a multilinear description, dL/dt={ L, M_1, ... , M_{N-2} }, automatically generating infinitely many conserved quantities, as…
In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.
In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…
The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…
This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…
The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly…
Inspired by Borcherds' questions, Guerzhoy constructed a new type of Hecke operators $\mathcal{T}(p)$, called the multiplicative Hecke operators, which acts on the space of meromorphic modular forms on the full modular group ${\rm SL}(\Z)$.…
For two positive integers m and n, we let ${\mathcal P}_n$ be the open convex cone in ${\mathbb R}^{n(n+1)/2}$ consisting of positive definite n x n real symmetric matrices and let ${\mathbb R}^{(m,n)}$ be the set of all m x n real…
QCD in non-integer d=4-2 epsilon space-time dimensions possesses a nontrivial critical point and enjoys exact scale and conformal invariance. This symmetry imposes nontrivial restrictions on the form of the renormalization group equations…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
The non-singlet and singlet anomalous dimensions of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O(\alpha_s)$. We apply these results for the derivation of evolution equations…
This paper is concerned with a parabolic evolution equation of the form $A(u_t) + B(u) = f$, settled in a smooth bounded domain of ${\bf R}^d$, $d \geq 1$, and complemented with the initial conditions and with (for simplicity) homogeneous…
Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q…