Related papers: Half-integral weight Eichler integrals and quantum…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
It is known that non-commutative fluids used to model the Fractional Quantum Hall effect give Calogero--Moser systems. The group-theoretic description of these as reductions of free motion on type A Lie algebras leads directly to Laughlin…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…
In this paper we introduce a certain space of higher order modular forms of weight 0 and show that it has a Hodge structure coming from the geometry of the fundamental group of a modular curve. This generalizes the usual structure on…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
In this paper we present rigorously and as succintly as possible the theory of elliptic quasi-modular forms by means of moduli spaces and the Gauss-Manin connection, and deal with one of the main historical appearances of quasi-modular…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
One of the main open problems in the theory of automorphic products is to classify reflective modular forms. In [Sch06] Scheithauer classified strongly reflective modular forms of singular weight on lattices of prime level. In this paper we…
We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are…
Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of…
This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…