Related papers: The universal path integral
We review recent results on the derivation of a global path integral density for Yang-Mills theory. Based on a generalization of the stochastic quantization scheme and its geometrical interpretation we first recall how locally a modified…
We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schr\"odinger state of a system in a Hilbert space of arbitrary dimensionality is…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
A Lagrangian description of the qubit based on a generalization of Schwinger's picture of Quantum Mechanics using the notion of groupoids is presented. In this formalism a Feynman-like computation of its probability amplitudes is done. The…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…