Related papers: A note on the path integral for systems with prima…
I consider the case of two interacting scalar fields, \phi and \psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…
We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with…
In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of…
Passive scalar transport in a spatially-extended background of roll convection is considered in the time-periodic regime. The latter arises due to the even oscillatory instability of the cell lateral boundary, here accounted for by…
We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interior gradient estimates for any constant phases.
Transition state theory formally provides a simplifying approach for determining chemical reaction rates and pathways. Given an underlying potential energy surface for a reactive system, one can determine the dividing surface in phase space…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
We explore the existence of a class of generalised Laplace maps for third order partial differential operators of the form…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
It is demonstrated that the nature of optical parametric amplification is a quantum phenomenon. The system Lagrangian can be constructed by the path integral of coherent state. The equations of motion for photon operators are indeed the…
The 2-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
In the extended Lagrange formalism of classical point dynamics, the system's dynamics is parametrized along a system evolution parameter $s$, and the physical time $t$ is treated as a \emph{dependent} variable $t(s)$ on equal footing with…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
A recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series, with an iterative selection of variables and time delays. A case study of numerically generated…
In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base…
The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…