Related papers: Path integral quantization of the relativistic Hop…
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 present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is…
We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…
The Floreanini-Jackiw formulation of the chiral quantum-mechanical system oscillator is a model of constrained theory with only second-class constraints. in the Dirac's classification.The covariant quantization needs infinite number of…
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White…
The path-integral measure of linearized gravity around a saddle-point background with the cosmological term is considered in order to study the conformal rotation prescription proposed by Gibbons, Hawking and Perry. It is also argued that…
The computation of anomalies in quantum field theory may be carried out by evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation of these Jacobians can be cast in the form of a quantum mechanical problem, whose…
After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of…
We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ) generalized brackets of the gauge invariant self-dual fields interacting with gauge fields. We further give FJ quantization of this system. Furthermore, the FJ…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response.…
In the present paper we study the Faddeev-Popov path integral quantization of electrodynamics in an inhomogenious dielectric medium. We quantize all polarizations of the photons and introduce the corresponding ghost fields. Using the heat…
We apply the Faddeev-Jackiw method to the Hamiltonian analysis of the massless spin-two field. As expected, the reduced Hamiltonian contains only the traceless-transverse tensor, while some, but not all of the non-propagating components are…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational fields at the Planck scale (2022 J. Phys. A: Math. Theor.55 105303). In the present study, we use the…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the…
In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional…
Basing on the canonical quantization of a BRS invariant Lagrangian, we construct holomorphic representation of path integrals for Faddeev-Popov(FP) ghosts as well as for unphysical degrees of the gauge field from covariant operator…