Local Quantum Physics

Facts and Fictions About Anti deSitter Spacetimes¶with Local Quantum Matter

“…But there is a hurdle right at the start: unlike QM where a quantization box defines a inside/outside division of the Hilbert space and the quantum mechanical algebra (type I ∞ von Neumann factor) through a tensor product factorization, the nature of the double cone algebras (the relativistic causally closed analogs of boxes) in QFT is totally different, since as hyperfinite type III 1 von Neumann factors they contain neither minimal projectors nor are there any pure states among its normal states [36]. This unusual state of affairs requires the introduction of the "split property" in order to construct the relativistic analogue of the QM box [16]. The physical mechanism behind this property is the strong vacuum fluctuations of partial charges at the surface of its localization volume V, one of the oldest and most characteristic phenomena which set apart QFT from QM.…”

Nonequilibrium Mesoscopic Conductors Driven by Reservoirs

“…Although they can be defined trivially for free electrons, it is nontrivial in the presence of many-body interactions. In high-energy physics, they are defined based on the asymptotic condition, which assumes that particles behave like free (but renormalized) ones as t → ±∞, i.e., before and after the collision [40]. For example, an electron (in the vacuum) before or after the collision becomes a localized "cloud" of electrons and positrons, which extend only over the Compton length, and this cloud can be regarded as a renormalized electron.…”

“…By puttingŶ α (r) ≡ d 3 r ′ ϕ ⊥ * (y, z; x)ψ Rα (r)v sc (r, r ′ )ψ † Rα (r ′ )ψ Rα (r ′ ) (for α = L, R), which differs fromŶ α of the impurity-scattering case, we obtain the equation of motion forζ 1 in the same form as Eq. (40). To derive the equation of motion forĪ from that equation, we need to calculate the correlation functions in the reservoirs, Ŷ α (t)Ŷ † α (t ′ ) α and Ŷ † α (t)Ŷ α (t ′ ) α .…”

Quantum Fields in Accelerated Frames

“…Even just this argument is sufficient to prove the inapplicability of the Unruh quantization scheme for investigation of the Minkowski vacuum. However, to make the picture complete, it is worth saying that the aforementioned necessity to cut out the wholeF andP wedges leads to nonexistence of correlations between fields in the wedges R and L. It is not trivial since such correlations are known to be present in the usual QFT in MS where their existence is manifested by general principles of QFT, for example by the Reeh-Schlieder theorem (see [9], theorem 5.3.2). In the latter case they arise when one prepares a Fock state, because both R and L wedges can be causally communicated from the wedge P .…”

“…Refs. [9,12]. In such approach a thermal state is defined as the one satisfying the Kubo-Martin-Schwinger (KMS) condition.…”