Related papers: Coordinate-Free Quantization of Second-Class Const…
We consider the problem of deep neural net compression by quantization: given a large, reference net, we want to quantize its real-valued weights using a codebook with $K$ entries so that the training loss of the quantized net is minimal.…
We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order $\Delta$-operator. Based on two conjugate higher-order $\Delta$-operators, we also propose a Lagrangian path integral with…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new…
Some recent results show that the covariant path integral and the integral over physical degrees of freedom give contradicting results on curved background and on manifolds with boundaries. This looks like a conflict between unitarity and…
We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras.…
Stiff forces, which bind objects together or otherwise confine motion, are found widely in soft-matter systems - colloids with short range attractions, ligand-receptor contacts, particles in optical traps, fibres that resist stretching,…
It is shown that the phase space of a dynamical system subject to second class constraints can be extended by ghost variables in such a way that some formal analogies of the $\Omega$-charge and the unitarizing Hamiltonian can be…
When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the…
BRST quantization is carried out for a model of p-branes with second class constraints. After extension of the phase space the constraint algebra coincides with the one of null string when p=1. It is shown that in this case one can or can…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
In this work, we investigate the quantum Brownian motion of a point charge arising as a consequence of two fluctuating point-like boundaries. The study considers Dirichlet, Neumann, and mixed boundary conditions imposed on a real massless…
The BRST quantization of particle motion on the hypersurface $V_{(N-1)}$ embedded in Euclidean space $R_N$ is carried out both in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) formalism, the second class…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
To appear in proceedings of II Workshop on ``Constraints Theory and Quantisation Methods''Montepulciano (Siena) 1993} General discussion of the constraints of 2+1 gravity, with emphasis on two approaches, namely the second order and first…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
In this series of papers, we present a set of methods to revive quantum geometrodynamics which encountered numerous mathematical and conceptual challenges in its original form promoted by Wheeler and De Witt. In this paper, we introduce the…
We show how additional constraints, restricting the spectrum of the optimized pulse or confining the system dynamics, can be used to steer optimization in quantum control towards distinct solutions. Our examples are multi-photon excitation…