Wick Rotation and Fermion Doubling in Noncommutative Geometry

In this paper, we discuss two features of the noncommmutative geometry and spectral action approach to the Standard Model: the fact that the model is inherently Euclidean, and that it requires a quadrupling of the fermionic degrees of freedom. We show how the two issues are intimately related. We give a precise prescription for the Wick rotation from the Euclidean theory to the Lorentzian one, eliminating the extra degrees of freedom. This requires not only projecting out mirror fermions, as has been done so far, and which leads to the correct Pfaffian, but also the elimination of the remaining extra degrees of freedom. The remaining doubling has to be removed in order to recover the correct Fock space of the physical (Lorentzian) theory. In order to get a Spin(1,3) invariant Lorentzian theory from a Spin(4) invariant Euclidean theory such an elimination must be performed after the Wick rotation. Differences between the Euclidean and Lorentzian case are described in detail, in a pedagogical way.Comment: Minor changes. To appear in PRD. 25 page

Formulation of blade-flutter spectral analyses in stationary reference frame

Analytic representations are developed for the discrete blade deflection and the continuous tip static pressure fields in a stationary reference frame. Considered are the sampling rates equal to the rotational frequency, equal to blade passing frequency, and for the pressure, equal to a multiple of the blade passing frequency. For the last two rates the expressions for determining the nodal diameters from the spectra are included. A procedure is presented for transforming the complete unsteady pressure field into a rotating frame of reference. The determination of the true flutter frequency by using two sensors is described. To illustrate their use, the developed procedures are used to interpret selected experimental results

Flutter spectral measurements using stationary pressure transducers

Engine-order sampling was used to eliminate the integral harmonics from the flutter spectra corresponding to a case-mounted static pressure transducer. Using the optical displacement data, it was demonstrated that the blade-order sampling of pressure data may yield erroneous results due to the interference caused by blade vibration. Two methods are presented which effectively eliminate this interference yielding the blade-pressure-difference spectra. The phase difference between the differential-pressure and the displacement spectra was evaluated

Turbofan compressor dynamics during afterburner transients

The effects of afterburner light-off and shut-down transients on compressor stability were investigated. Experimental results are based on detailed high-response pressure and temperature measurements on the Tf30-p-3 turbofan engine. The tests were performed in an altitude test chamber simulating high-altitude engine operation. It is shown that during both types of transients, flow breaks down in the forward part of the fan-bypass duct. At a sufficiently low engine inlet pressure this resulted in a compressor stall. Complete flow breakdown within the compressor was preceded by a rotating stall. At some locations in the compressor, rotating stall cells initially extended only through part of the blade span. For the shutdown transient, the time between first and last detected occurrence of rotating stall is related to the flow Reynolds number. An attempt was made to deduce the number and speed of propagation of rotating stall cells

Measurements of self-excited rotor-blade vibrations using optical dispacements

The characteristics of optical displacement spectra and their role of monitoring rotor blade vibrations are discussed. During the operation of a turbofan engine at part speed, near stall, and elevated inlet pressure and temperature, several vibratory instabilities were excited simultaneously on the first fan rotor. The torsional and bending contributions to the main flutter mode were resolved by using casing-mounted optical displacement sensors. Other instabilities in the blade deflection spectra were identified

The Gribov problem in Noncommutative QED

It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.Comment: 19 pages, 3 figures. Published. The paper has been shortened and many references have been judged unnecessary or not suitable during the reviewing proces

Higgs-Dilaton Lagrangian from Spectral Regularization

In this letter we calculate the full Higgs-Dilaton action describing the Weyl anomaly using the bosonic spectral action. This completes the work we started in our previous paper (JHEP 1110 (2011) 001). We also clarify some issues related to the dilaton and its role as collective modes of fermions under bosonization

Spectral Regularisation: Induced Gravity and the Onset of Inflation

Using spectral regularisation, we compute the Weyl anomaly and express the anomaly generating functional of the quantum effective action through a collective scalar degree of freedom of all quantum vacuum fluctuations. Such a formulation allows us to describe induced gravity on an equal footing with the anomaly-induced effective action, in a self-consistent way. We then show that requiring stability of the cosmological constant under loop quantum corrections, Sakharov's induced gravity and Starobinsky's anomaly-induced inflation are either both present or both absent, depending on the particle content of the theory.Comment: 23 pages, 1 figure Slightly amended file to match published versio

Synthesis of blade flutter vibratory patterns using stationary transducers

Flutter frequency was determined and rotor vibratory amplitude and phase distributions during flutter were reconstructed from stationary aerodynamic type measurements. A previously reported optical method for measuring blade-tip displacement during flutter was extended by means of digital analysis. Displacement amplitudes and phase angles were determined based on this method. For selected blades, spectral results were also obtained from strain gage measurements. The results from these three types of measurement were compared and critically evaluated

Spectral Action from Anomalies

Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another term to the action. This term comes out to be basically the Chamseddine Connes spectral action introduced in the context of noncommutative geometry. An alternative realization of the dilaton may involve a collective scalar mode of all fermions accumulated in a {scale-noninvariant} dilaton action. The entire spectral action describes gauge and Higgs fields coupled with gravity. Here this action is coupled with a dilaton and we discuss how it relates to the transition from the radiation to the electroweak broken phase via condensation of Higgs fields.Comment: Proceedings of the Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity, September 8-12, 2010 Corfu Greec