Related papers: Gauge-covariant stochastic neural fields: Stabilit…
We develop a gauge-invariant formalism to describe metric perturbations in five-dimensional brane-world theories. In particular, this formalism applies to models originating from heterotic M-theory. We introduce a generalized longitudinal…
Gauge-invariant field strengths, defined as parallel transports to infinity of ordinary field strengths, naturally emerge in a few physical phenomena governed by $QCD$. One of them is confinement of colour. Despite the arbitrariness in…
In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition…
We show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\mathbb{R}^3_\lambda$ and the components of…
We study covariant open bosonic string field theory in lightcone gauge. When lightcone gauge is well-defined, we find two results. First, the vertices of the gauge-fixed action consist of Mandelstam diagrams with stubs covering specific…
Phenomenological analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings, plasmon and…
This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…
Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but…
The use of proper time as a tool for causality implementation in field theory is clarified and extended to allow a manifestly covariant definition of discrete fields proper to be applied in field theory and quantum mechanics. It implies on…
The main objective of the paper is to study the long-time behavior of general discrete dynamics driven by an ergodic stationary Gaussian noise. In our main result, we prove existence and uniqueness of the invariant distribution and exhibit…
This paper is the second in the series Commutative Scaling of Width and Depth (WD) about commutativity of infinite width and depth limits in deep neural networks. Our aim is to understand the behaviour of neural functions (functions that…
We explain how the spacetime diffeomorphism in the classical bosonic closed string field theory (SFT) is represented as $L_\infty$ gauge transformations in weakly curved backgrounds. In particular, we demonstrate the explicit map between…
Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…
The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume…
We set up the effective field theories which describe the SO(5)-invariant picture of the high-Tc cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5)-breaking effects. We consider two…
Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently, as they provide a clear analytical window to deep learning via mappings to Gaussian Processes (GPs). Despite its theoretical appeal, this…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone…
For large values of the Higgs mass the low energy structure of the gauged linear sigma model in the spontaneously broken phase can adequately be described by an effective field theory. We present a manifestly gauge-invariant functional…
We construct off-shell amplitudes in heterotic and type II string theories involving arbitrary combination of Ramond and Neveu-Schwarz sector external states. We also construct the equations of motion of a gauge invariant 1PI effective…