Related papers: A Lagrangian path integral approach to the qubit
Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this…
We show that the Feynman path integral together with the Schr\"odinger representation gives rise to a rigorous and functorial quantization scheme for linear and affine field theories. Since our target framework is the general boundary…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
Using Feynman's representation of the quantum evolution and considering a quantum particle as a matter field (continuous medium), it is shown that individual particles of the field have unique paths of the motion. This allows describing…
This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian…
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…
Applications of the Path Group (consisting of classes of continuous curves in Minkowski space-time) to gauge theory and gravity are reviewed. Covariant derivatives are interpreted as generators of an induced representation of Path Group.…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle…
Hamilton's action principle is formulated and extended in conformity with the gauge transformations underlying Weyl's geometry. The extended principle characterizes infinitely many equally likely trajectories with a particle traveling along…
The given article example of physical analogies to be entered information space-time. The opportunity of Poincare group use is shown for transition from one frame in another, for this purpose is entered invariant velocity of transition of…
Given a directed graph E we describe a method for constructing a Leavitt path algebra $L_R(E)$ whose coefficients are in a commutative unital ring R. We prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness Theorem…
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and…
We formalize Feynman's construction of the quantum mechanical path integral. To do this, we shift the emphasis in differential geometry from the tangent bundle onto the pair groupoid. This allows us to use the van Est map and the piecewise…
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time…
The standard formulation of gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic qunantum theoretical access in the spirit of Wigner's representation theory shows that…
The path integral formulation of singular systems with second order Lagrangian is studied by using the canonical path integral method. The path integral of Podolsky electrodynamics is studied.
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…