Related papers: Density Formalism for Quantum Theory
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
Quantum electrodynamics is the well-accepted theory. However, we feel it is useful to look at formalisms that provide alternative ways to describe light, because in the recent years the development of quantum field theories based primarily…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…
This text aims to explains briefly the formalism of quantum mechanics to mathematicians.
Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse…
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…
We show how to compute the purity and entanglement entropy for quantum fields in a systematic perturbative expansion. To that end, we generalize the in-in formalism to non-unitary dynamics (i.e. accounting for the presence of an…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.