Classical Topology and Quantum States
نویسنده
چکیده
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘Quantum Mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its CK− and C∞− structures) can be reconstructed using Gel’fand Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed. ∗Talk presented at the Winter Institute on Foundations of Quantum Theory and Quantum Optics,S.N.Bose National Centre for Basic Sciences,Calcutta,January 1-13,2000.
منابع مشابه
بررسی خواص کوانتومی حالتهای همدوس دومدی درهمتنیده
Coherent states are the quantum states, which give the closest description to classical states. Since their superpositions show quantum properties, research on these states has been of great interest. In addition, having nonclassical properties is necessary for quantum correlations. In this paper, we focus on two-mode entangled coherent states which are out of phase, and study the nonclassical...
متن کاملفرمولبندی هندسی کوانتش تغییرشکل برزین
In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...
متن کاملدینامیک کوانتومی ذره جرمدار روی دوسیتر 3+1
The phase space which is related to the motion of massive particle on 1+3- De sitter space is a 3-dimensional complex sphere. Our main aim in this study is discribing this movement in the frame quantum mechanics. Transfering from classical mechanic to quantum mechanics is possible by means of coherent states. Thus, after determination of this state, we quantize some of the classical observables.
متن کاملTopology Change and Quantum Physics
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several ex...
متن کاملCoherent Transport of Single Photon in a Quantum Super-cavity with Mirrors Composed of Λ-Type Three-level Atomic Ensembles
In this paper, we study the coherent transport of single photon in a coupled resonator waveguide (CRW) where two threelevel Λ-type atomic ensembles are embedded in two separate cavities. We show that it is possible to control the photon transmission and reflection coefficients by using classical control fields. In particular, we find that the total photon transmission and reflection are achieva...
متن کامل