Related papers: Probability representation in quantum field theory
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
We discuss how the classical notions of time and causal structure may emerge together with quantum-mechanical probabilities from a universal quantum state. For this, the process of decoherence between semiclassical branches is important.…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the…
An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for…
We report on recent results on the Quantum Field Theory of mixed particles. The quantization procedure is discussed in detail, both for fermions and for bosons and the unitary inequivalence of the flavor and mass representations is proved.…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…
The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum…