Related papers: Path integrals for the relativistic particle: Some…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
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…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.
Lattice QCD should allow quantitative predictions for the heavy quark physics from first principles. Up to now, however, most approaches have based on the nonrelativistic effective theory, with which the continuum limit can not be taken in…
We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the na\"ive continuum limit but which, nevertheless, induce non-trivial effects due to quantum…
Starting from well-known expressions for the $T$-matrix and its derivative in standard nonrelativistic potential scattering I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a previously unnoticed symmetry, which is present for any Lagrangian term that involves $\dot{x}^2$. As a basic model that incorporates…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for…
Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting…
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi…