相关论文: Path integrals from classical momentum paths

The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…

We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…

Inspired by the usefulness of local scaling of time in the path integral formalism, we introduce a new kind of hamiltonian path integral in this paper. A special case of this new type of path integral has been earlier found useful in…

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…

Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized…

Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely…

On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…

We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for…

This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure…

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…

A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…

Power duality in Feynman's path integral formulation of quantum mechanics is investigated. The power duality transformation consists of a change in coordinate and time variables, an exchange of energy and coupling, and a classical angular…

Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…

A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…

A path integral method, combined with atomistic spin dynamics simulations, has been developed to calculate thermal quantum expectation values using a classical approach. In this study, we show how to treat Hamiltonians with non-linear…

We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…

The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…

We formulate path integrals on any Riemannian manifold which admits the action of a compact Lie group by isometric transformations. We consider a path integral on a Riemannian manifold M on which a Lie group G acts isometrically. Then we…