Related papers: Conformal Foliations and Constraint Quantization
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
An alternative representation of the kernel of the evolution operator in quantum electrodynamics is obtained in the form of a functional integral, in which the gauge momentum corresponding to the Gaussian constraint is excluded from the…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
We study the properties of a non-abelian gauge theory subjected to a gauge invariant constraint given by the classical equations of motion. The constraint is not imposed by hand, but appears naturally when we study a particular type of…
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis' formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of…
In the companion paper arXiv:2110.05298, we developed the deformation theory of symplectic foliations, focusing on geometric aspects. Here, we address some algebraic questions that arose naturally. We show that the $L_{\infty}$-algebra…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the…
The correlators of two-dimensional rational conformal field theories that are obtained in the TFT construction of [FRSI,FRSII,FRSIV] are shown to be invariant under the action of the relative modular group and to obey bulk and boundary…
In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
The pseudo--rigid body represents an example of a constrained system with a nonunimodular gauge group. This system is treated along the guidelines of an algebraic constraint quantization scheme which focusses on observable quantities,…
It is well known that --differing from ordinary gauge systems-- canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…