Related papers: Effective Action in Free Probability
The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of…
We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective…
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations…
While free and weakly interacting nonrelativistic particles are described by a Gross-Pitaevskii equation, which is a nonlinear self-interacting Schr\"odinger equation, the phenomena in the strong- coupling limit are governed by an effective…
The connection between the Hamilton and the standard Lagrange formalism is established for a generic Quantum Field Theory with vanishing vacuum expectation values of the fundamental fields. The Effective Actions in both formalisms are the…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator…
Von Neumann's statistical theory of quantum measurement interprets the instantaneous quantum state and derives instantaneous classical variables. In realty, quantum states and classical variables coexist and can influence each other in a…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
The 1/N expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the 1/N expansion in the O(N) model by comparing…
An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations…
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonically associated to the \textbf{standard semi--circle random…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
The aim of this paper is to construct a quantum effective action for gravitational fields by the effective potential method in quantum field theory. The minimum of the quantum effective action gives an equation of quantum fluctuations. We…
Fluctuations can challenge the possibility of improving work extraction from quantum correlations. This uncertainty in the work extraction process can be addressed resorting to the expected utility hypothesis which can provide an optimal…