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Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Particle creation by strong and time-varying backgrounds is a robust prediction of quantum field theory. Another well-established feature of field theory is that classical symmetries do not always extend to the quantized theory. When this…
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…
We reconstruct finite-dimensional quantum theory with superselection rules, which can describe hybrid quantum-classical systems, from four purely operational postulates: symmetric sharpness, complete mixing, filtering, and local equality.…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the…
The problem of measurement in quantum mechanics is that the quantum particle in the course of evolution, as described by the linear Schrodinger equation, exists in all of its possible states, but in measuring, the particle is always…
After having explained Samuel Clarke's conception of the new philosophy of physical reality, we will treat the electron field in this context as a field modifying the void. From this we will be able to derive the so-called quantum rules…
Particle production by expanding in the future light cone scalar quantum field is studied by assuming that the initial state is associated with the quasiequilibrium statistical operator corresponding to fluid dynamics. We calculate particle…
This article introduces Universal Quantum Relativity which is a simple Theory of Everything. It relies on an ultimate doctrine that is the absence of absolute existence. This generalizes relativity principles up to a mother quantum theory.…
According to classical physics particles are basic building blocks of the world. Classical particles are distinguishable objects, individuated by physical characteristics. By contrast, in quantum mechanics the standard view is that…