Related papers: Path integral quantization of the relativistic Hop…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole…
The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one…
The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
Using the Schwinger-Keldysh path integral, we draw a connection between localized quantum field theories and more commonly used models of local probes in Relativistic Quantum Information (RQI). By integrating over and then tracing out the…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
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.…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
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…
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…
The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev--Popov) path integral quantization (Matthews's theorem) is proven for gauge theories with arbitrary effective interaction terms. Effective gauge-boson self-interactions…
We demonstrate an original development of path-integral quantization in the case of a multiply connected configuration space of indistinguishable charged particles on a 2D manifold and exposed to a strong perpendicular magnetic field. The…
The eletromagnetic field in a linear absorptive dielectric medium, is quantized in the framework of the damped polarization model. A Hamiltonian containing a reservoir with continuous degrees of freedom, is proposed. The reservoir minimally…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…