Related papers: Path integral in energy representation in quantum …
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
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…
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…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and…
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.…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
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…
We introduce two new integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories…