Related papers: Critical Review of Path Integral Formulation
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
Compared to classical optical coherence theory based on Maxwell's electromagnetic theory and Glauber's quantum optical coherence theory based on matrix mechanics formulation of quantum mechanics, quantum optical coherence theory based on…
We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables.…
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…
Following the idea of Alekseev and Shatashvili we derive the path integral quantization of a modified relativistic particle action that results in the Feynman propagator of a free field with arbitrary spin. This propagator can be associated…
The possibility of extending the canonical formulation of quantum mechanics (QM) to a space-time symmetric form has recently attracted wide interest. In this context, a recent proposal has shown that a spacetime symmetric many-body…
We discuss the path integral representation for the fermionic particles and strings and concentrate at the problems arising when some target-space dimensions are compact. An example of partition function for fermionic particle at finite…
We compute the quantum vacuum polarization for a pure neutral scalar field theory within the context of single-particle quantum mechanics. The loop diagram is computed without ever encountering loop-momentum integrals. Our approach is based…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
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.…
The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
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.…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…
Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…