Related papers: Loop groups and quantum fields
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual)…
Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Within the Quantum Action Principle framework we show the perturbative renormalizability of previously proposed topological lagrangian \`a la Witten-Fujikawa describing polymers, then we perform a 2 loop computation. The theory turns out to…
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
The 1-d Schrodinger flow on 2-sphere, the Gauss-Codazzi equation for flat Lagrangian submanifolds in C^n, and the space-time monopole equation are all examples of geometric soliton equations. The linear systems with a spectral parameter…
For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use…
This is a study of orbifold-quotients of quantum groups (quantum orbifolds $\Theta \rightrightarrows G_q$). These structures have been studied extensively in the case of the quantum $SU_2$ group. I will introduce a generalized mechanism…
The dissertation deals with noncommutative field theories, namely field theories compatible with the existence of a minimal (quantum gravity) length scale. Two families of quantum spacetime are considered. One is characterized by semisimple…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in…
Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a non-zero cosmological constant $\Lambda$ in this context has been a withstanding problem. Other approaches, such as Chern-Simons gravity, suggest…
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. to representation theory and irreducible representations of the Poincar'e group. Also, we tried to get a more comprehensible…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…