Related papers: Observables and unobservables in a non-associative…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some…
This paper argues that non-self-adjoint operators can be observables. There are only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these…
A model of quantum field theory in which the field operators form a nonassociative algebra is proposed. In such a case, the n-point Green's functions become functionally independent of each other. It is shown that particle interaction in…
The associators/antiassociators for the product of four non-associative operators are deduced. By analogy with SU(3) gauge theory the notion of colorless (white) operators is introduced. Some properties of white operators are considered. It…
Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…
A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with…
Toy models of a non-associative quantum mechanics are presented. The Heisenberg equation of motion is modified using a non-associative commutator. Possible physical applications of a non-associative quantum mechanics are considered. The…
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause…
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of strongly nonlinear field can form a non-associative algebra. It is shown that such algebra can be described as an algebra of…
A nonperturbative quantization procedure based on a nonassociative decomposition of quantum field operators on nonassociative constituents is considered. It is shown that such approach gives rise to quantum corrections by calculations of…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…
The interpretation of quantum theory known as QBism argues that many elements of the formalism have a subjective interpretation. At the same time, QBism claims to be a broadly realist program. This implies that reality in QBism must be…
A nonassociative generalization of supersymmetry is studied, where supersymmetry generators are considered to be the nonassociative ones. Associators for the product of three and four multipliers are defined. Using a special choice of the…
Practically measurable quantities resulting from quantum field theory are not described by hermitian operators, contradicting one of the cornerstone axioms of orthodox quantum theory. This could be a sign that some of the axioms of orthodox…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…