Related papers: Quantization conditions from the group theory

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…

We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…

In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered…

The Lorentz-covariant quantization performed in the Hamiltonian path-integral formalism for massless non-Abelian gauge fields has been achieved. In this quantization, the Lorentz condition, as a constraint, must be introduced initially and…

The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The resulting leads to a valid affine quantization of the particle in a box field theory, which points toward…

In this note we define the stabilizer group of any adjoint-invariant $l$-form on a complex simple Lie algebra. This result partially extend a previous result by Kable.

Pusey, Barrett and Rudolph (PBR) have recently given a completely novel argument that restricts the class of possible models for quantum phenomena (arXiv:1111.3328). In these notes the assumptions used by PBR are considerably weakened, to…

There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality…

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…

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions…

The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered…

Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extended here to instant- and…

We study the behavior of the variational eigenvalues of the p-Laplace operator, with homogeneous Dirichlet boundary condition, when p is varying. After introducing an auxiliary problem, we characterize the continuity answering, in…

We show that under certain conditions the Gelfand-Kazhdan criterion for the Gelfand property is a necessary condition. We work in the generality of finite groups, however part of the argument carries over to p-adic and real groups.

Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…

The limiting transitions between different types of quantizations are studied by the deformation theory methods. We prove that for the first order coboundary deformation (g,g*_1 + x g*_2) of a Lie bialgebra (g,g*) one can always get the…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force…

Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…