Related papers: Transition probability and preferential gauge
We derive a Hamiltonian formulation of the theory of gauge invariant, linear perturbations in anisotropic Bianchi I spacetimes, and describe how to quantize this system. The matter content is assumed to be a minimally coupled scalar field…
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The…
We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the $\bs{x}$ and $\bs{p}$ appearing in the Hamiltonian,…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…
The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary…
We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of…
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions…
We propose an efficient variational method for $Z_2$ lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge…
In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…
We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
We compare a recent excitation chain argument for the glass transition with the earlier random first order transition theory. The key equation determining the activation barriers and size of cooperatively rearranging regions has the same…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…