Quantum Fields a la Sylvester and Witt

A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling constants are normalizations of Lorentz invariantly embedded little groups (spin and polarization) arising in a harmonic analysis of quantum vector fields. It is shown that the harmonic analysis of massless fields requires an extension of the familiar Fourier decomposition, containing also indefinite unitary nondecomposable time representations. This is illustrated by the nonprobabilistic contributions in the electromagnetic field.Comment: 18 pages LaTeX file (62 kB), all macros are include

Realizations of Causal Manifolds by Quantum Fields

Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the homogenous spaces \D(n)=\GL(\C^n_\R)/\U(n) with $n=1$ for mechanics and $n=2$ for relativistic fields. The rank $n$ gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e. two characteristic masses in the relativistic case. 'Canonical' field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifold \D(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable - in addition to representations with eigenvectors (states, particle) they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field.Comment: 36 pages, latex, macros include

The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model

The correlation of the fractionally represented hypercharge group with the isospin and colour group in the standard model determines as faithfully represented internal group the quotient group {\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}. The discrete cyclic central abelian-nonabelian internal correlation involved is considered with respect to its consequences for the representations by the standard model fields, the electroweak mixing angle and the symmetry breakdown. There exists a further discrete $\Z_2$-correlation between chirality and Lorentz properties and also a continuous \U(1)-external-internal one between hyperisospin and chirality.Comment: 18 pages, latex, macros include

Real null coframes in general relativity and GPS type coordinates

Based on work of Derrick, Coll, and Morales, we define a `symmetric' null coframe with {\it four real null covectors}. We show that this coframe is closely related to the GPS type coordinates recently introduced by Rovelli.Comment: Latex script, 9 pages, 4 figures; references added to work of Derrick, Coll, and Morales, 1 new figur

Simplicial quantum dynamics

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.Comment: 25 pages. 1 table. Conference of the International Association for Relativistic Dynamics, Taiwan, 201

A case series on the value of tau and neurofilament protein levels to predict and detect delirium in cardiac surgery patients

BACKGROUND: Delirium following cardiac surgery is a relevant complication in the majority of elderly patients but its prediction is challenging. Cardiopulmonary bypass, essential for many interventions in cardiac surgery, is responsible for a severe inflammatory response leading to neuroinflammation and subsequent delirium. Neurofilament light protein (NfL) and tau protein (tau) are specific biomarkers to detect neuroaxonal injury as well as glial fibrillary acidic protein (GFAP), a marker of astrocytic activation. METHODS: We thought to examine the perioperative course of these markers in a case series of each three cardiac surgery patients under off-pump cardiac arterial bypass without evolving delirium (OPCAB-NDEL), patients with a procedure under cardio-pulmonary bypass (CPB) without delirium (CPB-NDEL) and delirium after a CPB procedure (CPB-DEL). Delirium was diagnosed by the Confusion Assessment Method for the ICU and chart reviews. RESULTS: We observed increased preoperative levels of tau in patients with later delirium, whereas values of NfL and GFAP did not differ. In the postoperative course, all biomarkers increased multi-fold. NfL levels sharply increased in patients with CPB reaching the highest levels in the CPB-DEL group. CONCLUSION: Tau and NfL might be of benefit to identify patients in cardiac surgery at risk for delirium and to detect patients with the postoperative emergence of delirium