Related papers: Integral transforms of the quantum mechanical path…
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…
I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the…
The single-particle inclusive differential cross-section for a reaction $a+b\to c+X$ is written as the imaginary part of a correlation function in a for ward scattering amplitude for $a+b\to a+b$ in a modified effective theory. In this…
We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional double-barrier step (PDBS) options, the option price changing process is analogous to a particle moving in a finite symmetric…
Mensky has suggested to account for "continuous measurement" by attaching to a path integral a weight function centered around the classical path that the integral assigns a probability amplitude to. We show that in fact this weight…
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…
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…
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…
We show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
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…
We establish a necessary and sufficient condition for averages over complex valued weight functions on R^N to be represented as statistical averages over real, non-negative probability weights on C^N. Using this result, we show that many…
In this article we will explore the concept of speedrunning as a representation of a simplified version of quantum mechanics within a classical simulation. This analogy can be seen as a simplified approach to understanding the broader idea…