Related papers: Holomorphic Quantization on the Torus and Finite Q…

Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time tau = t+z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be…

In quantum gravity the unitary evolution does not follow from the Wheeler-DeWitt dynamics equation as it follows from the Schr\"odinger equation in non-relativistic quantum mechanics. Therefore we can define a spin-foam model based on…

Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological…

Let $\rho: SL(2,\mathbb{Z})\to GL(2,\mathbb{C})$ be an irreducible representation of the modular group such that $\rho(T)$ has finite order $N$. We study holomorphic vector-valued modular forms $F(\tau)$ of integral weight associated to…

Let $\mathcal{A}$ be a Hom-finite additive Krull-Schmidt $k$-category where $k$ is an algebraically closed field. Let ${\rm mod} \mathcal{A}$ denote the category of locally finite dimensional $\mathcal{A}$-modules, that is, the category of…

Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras…

The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C). In the construction there appears a sign…

We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…

The most common quantization scheme in which to study a conformal field theory is radial quantization, wherein a Hilbert space of states is defined on a sphere, whose Hamiltonian when mapped to the plane is the dilatation generator and…

This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is…

We study the formal geometric quantization of $b^m$-symplectic manifolds equipped with Hamiltonian actions of a torus $T$ with nonzero leading modular weight. The resulting virtual $T$-modules are finite dimensional when $m$ is odd, as in…

Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…

The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…

Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in…

The $n$-dimensional quantum torus $\mathcal O_{\mathbf q}((F^\times)^n)$ is defined as the associative $F$-algebra generated by $x_1, \cdots, x_n$ together with their inverses satisfying the relations $x_ix_j = q_{ij}x_jx_i$, where $\mathbf…

There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…

This paper is a continuation of "Quantization of Lie bialgebras, III" (q-alg/9610030, revised version). In QLB-III, we introduced the Hopf algebra F(R)_\z associated to a quantum R-matrix R(z) with a spectral parameter, and a set of points…

We develop the theory of $L^2$-torsion of an automorphism of a group and compute it for every automorphism of a group which is hyperbolic and one-ended relative to a finite collection of virtually polycyclic groups. We also prove a…

Let $Top_c$ be the category of compact spaces and continuous maps and $Top_f\subset Top_c$ be the full subcategory of finite spaces. Consider the covariant functor $Mor:Top_f^{op}\times Top_c\to Top_c$ that associates any pair $(X,Y)$ with…