Related papers: Renormalized Path Integral in Quantum Mechanics
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR…
The restricted-path-integral (RPI) theory of continuous quantum measurements including the evolution of the measured systems and phenomenon of decoherence is reviewed. The measured system is considered as an open quantum system but without…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
In prior work \cite{AD} of Lars Andersson and Bruce K. Driver, the path space with finite interval over a compact Riemannian manifold is approximated by finite dimensional manifolds $H_{x,\P} (M)$ consisting of piecewise geodesic paths…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
A geometric representation is found for the previously obtained path integral reduction Jacobian in Wiener-type path integral when quantizing a model mechanical system, which is used to describe the motion of two interacting scalar…
We reconstruct quantum mechanics by introducing "information operators" and excluding the concept of wave functions. Multiple information operators simultaneously describe a single system and continuously develop in time even in the process…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
The computation of anomalies in quantum field theory may be carried out by evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation of these Jacobians can be cast in the form of a quantum mechanical problem, whose…
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact,…
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector.…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable…
Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple…