LIGHTFRONT FORMALISM VERSUS HOLOGRAPHY&CHIRAL SCANNING

Abstract

The limitations of the approach based on using fields restricted to the lightfront (Lightfront Quantization or p→ ∞ Frame Approach) which drive quantum fields towards canonical and ultimately free fields are well known. Here we propose a new concept which does not suffer from this limitation. It is based on a procedure which cannot be directly formulated in terms of pointlike fields but requires "holographic" manipulations of the algebras generated by those fields. We illustrate the new concepts in the setting of factorizable d=1+1 models and show that the known fact of absence of ultraviolet problems in those models (in the presence of higher than canonical dimensions) also passes to their holographic images. In higher spacetime dimensions d>1+1 the holographic image lacks the transversal localizability; however this can be remedied by doing holography on d-2 additional lightfronts which share one lightray (Scanning by d-1 chiral conformal theories).

Holography and SL(2,ℝ) symmetry in 2D Rindler space–time

“…In that paper we show that, in fact, a suitable and natural enlargement in the Fock space of the hidden SL ( Essentially speaking, this is due to the behavior of n-point functions on the Killing horizon which is not Hadamard. In this context it would be interesting to investigate the holographic meaning of the Hadamard states (Minkowski vacuum and Hartle-Hawking state) also to make contact with results found in [15,16,17,18] where the net of Von Neumann algebras are defined with respect to Hadamard states.…”

“…They even use the term "hidden symmetry" a sense similar as we do here and we done in [1]. In related follow-up works by Schroer [17] and by Schroer and Fassarella [18] the relation to holography and diffeomorphism covariance is also discussed.…”

The paradigm of the area law and the structure of transversal and longitudinal lightfront degrees of freedom

“…For the convenience of the reader we have collected the previously presented results on lightfront restrictions of free fields as well as some geometric definitions concerning lightfront, wedges and their lightfront-horizon [5] [34] in compressed form in an appendix. The reader is strongly advised to have a look at the results obtained by this mathematically more elementary lightfront restriction method (which is limited to free fields) before he reads the next section.…”

Wigner particle theory and local quantum physics

“…For such models PFG generators of wedge algebras are (as a result of their nontemperedness) too singular objects. One either must hope to find different (non-PFG) generators, or use other modular methods [20] related to holographically defined modular inclusions or modular intersections. For example holographic lightfront methods are based on the observation that the full content of a ddimensional QFT can be encoded into d-1 copies of one abstract chiral theory whose relative placement in the Hilbert space of the d-dimensional theory carries the information.…”

“…Therefore it is a bit misleading to say that local quantum physics is just QM with the nonrelativistic Galilei group replaced by Poincaré symmetry; these two requirements would lead to the relativistic QM mentioned in the previous section whereas QFT is characterized by microcausality of observables and modular localization of states. To avoid any misunderstanding, projectors in compact causally closed local regions O of course exist, but they necessarily describe fuzzy (non sharp) localization within O [20] and the vacuum is necessarily a highly entangled temperture state if restriceted via this projector (in QM spatial restrictions only create isotopic representations i.e. enhanced multiplicities but do not cause genuine entanglement or thermal behavior).…”