Related papers: Relativistic few-body physics
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
The Hilbert space of the unitary irreducible representations of a Lie group that is a quantum dynamical group are identified with the quantum state space. Hermitian representation of the algebra are observables. The eigenvalue equations for…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
The principles of the physical description of non-inertial frames of reference are analyzed. The systems of physical reality description (PhRD) are introduced on base of generalization of the relativistic principle in special and general…
We study a quantum mechanics with the usual postulates but in which the Heisenberg algebra of canonical commutation relations and the Poincare algebra are replaced by the Lie algebra of the homogeneous Lorentz group SO(5,1). It arises from…
We present a new interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincar\'e group. We argue that the…
These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role…
We construct Quantum Representation Theory which describes quantum analogue of representations in frame of "non-commutative linear geometry" developed by Manin. To do it we generalise the internal hom-functor to the case of adjunction with…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it…
We review the recently proposed unreduced, complex-dynamical solution to the many-body problem with arbitrary interaction and its application to the unified solution of fundamental problems, including dynamic foundations of causally…