Related papers: Inequivalent Vacuum States in Algebraic Quantum Th…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
An algebraic characterization of vacuum states in Minkowski space is given which relies on recently proposed conditions of geometric modular action and modular stability for algebras of observables associated with wedge-shaped regions. In…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. An one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT)…
Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies…
It is discussed a truncation of the kinematical Hilbert space of Loop Quantum Gravity, which describes the dynamical system associated with an inhomogeneous cosmological model.
On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. This is a brief review in which we consider the problem for states in infinite dimensional Hilbert spaces.…
A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have…
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…