Related papers: BRST invariant approach to quantum mechanical tunn…
We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from…
An approximate approach to quantum vibrational dynamics, "Brownian Chain Molecular Dynamics (BCMD)", is proposed to alleviate the chain resonance and curvature problems in the imaginary time-based path integral (PI) simulation. Here the…
Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP)…
Hamiltonian BRST formalism (FV formalism) includes many auxiliary fields without explanation. Its path-integration has a simple form by using BRST charge, but its construction is quite mechanically and hard to understand physical meaning.…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem…
The quantum action (dynamical) principle is exploited to investigate the nature and origin of the Faddeev-Popov (FP) factor in gauge theories without recourse to path integrals. Gauge invariant as well as gauge non-invariant interactions…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The…
Several path integral representations for the $T$-matrix in nonrelativistic potential scattering are given which produce the complete Born series when expanded to all orders and the eikonal approximation if the quantum fluctuations are…
The tunneling method for stationary black holes in the Hamilton-Jacobi variant is reconsidered in the light of various critiques that have been moved against. It is shown that once the tunneling trajectories have been correctly identified…
A topological gauge invariant lagrangian for Seiberg-Witten monopole equations is constructed. The action is invariant under a huge class of gauge transformations which after BRST fixing leads to the BRST invariant action associated to…
We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space}…
In this paper we study the gauge invariance of the third quantized super-group field cosmology which is a model for multiverse. Further, we propose both the nfinitesimal (usual) as well as the finite superfield-dependent BRST symmetry…
The geometric interpretation of the Batalin-Vilkovisky antibracket as the Schouten bracket of functional multivectors is examined in detail. The identification is achieved by the process of repeated contraction of even functional…
We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
We present the generalization to non positive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original…
This article presents a review on the theoretical and the experimental developments on macroscopic quantum tunneling and phase transition of the escape rate in spin systems. We present the basic ideas with simplified calculations so that it…
The modified Becke-Johnson exchange potential combined with local-density approximation correlation (mBJLDA) has recently attracted interest because it provides highly improved band gaps at a very low computational cost. In this work we…