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Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…
In the present paper, we consider in detail the aspects of the Heisenberg's equations of motion, related to their transformation to the representation dependent of external sources. We provide with a closed solution as to the…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to…
Path integral formulation of quantum mechanics (and also other equivalent formulations) depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
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…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
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…
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…
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…
When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…
This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some…
The Fokker_Planck equation can be derived in a consistent manner through a microscopic approach based on a unified scheme of classical and quantum mechanics. Here we shall derive it through a purely quantum mechanical approach based on the…
The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither…