Quantum Gravity Equation In Schroedinger Form In Minisuperspace Description

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.Comment: 11 Pages, ReVTeX, no figur

Consistency of Semiclassical Gravity

We discuss some subtleties which arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga-Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2

Advances in Computer Reconstruction of Acoustical Holography

The article describes the results of two methods: the Fresnel approximation and the convolution method used for the exact Rayleigh-Sommerfeld equation. Curves for the Fresnel approximation are shown as a function of flaw depth and number of sample points. Despite a violation of the fresnel condition, an image can be achieved without visible phase distortion. This and its limits are shown on synthetic and experimental data. By shifting the hologram and not changing the symmetric phase factor, calculation time is saved because the rearrangement in the image space is achieved automatically. The exact method angular spectrum has been simplified in three steps. For different insonification angles in shear wave holography, the data set must be multiplied by an aperture function before being Fourier transformed. Examples demonstrate the usefulness of contact technique probes. To improve the recording time, a 140 element array will be multiplexed electronically and moved mechanically

Time in Quantum Gravity

The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler-DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schroedinger-Wheeler-DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle-Hawking or wormhole dominance proposal boundary condition. We thus find an answer to the small scale boundary conditions.Comment: 12 Pages, LaTeX, no figur

Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton

We suggest a path integral formulation for the tunneling cosmological state, which admits a consistent renormalization and renormalization group (RG) improvement in particle physics applications of quantum cosmology. We apply this formulation to the inflationary cosmology driven by the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. In this way a complete cosmological scenario is obtained, which embraces the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution of the inflaton field and the ongoing generation of the Cosmic Microwave Background (CMB) spectrum on this background. Formation of this probability peak is based on the same RG mechanism which underlies the generation of the CMB spectrum which was recently shown to be compatible with the WMAP data in the Higgs mass range $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$. This brings to life a convincing unification of quantum cosmology with the particle phenomenology of the SM, inflation theory, and CMB observations.Comment: 18 pages, 3 figures, LaTe

Semiclassical approximation to supersymmetric quantum gravity

We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem \Sigma$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bosonic case, are discussed.Comment: 34 pages, clarifications added, typos correcte

Ultrasound mapping of lymph node and subcutaneous metastases in patients with cutaneous melanoma: Results of a prospective multicenter study

Background: Ultrasound (sonography, B-mode sonography, ultrasonography) examination improves the sensitivity in more than 25% compared to the clinical palpation, especially after surgery on the regional lymph node area. Objective: To evaluate the distribution of metastases during follow-up in the draining lymph node areas from the scar of primary to regional lymph nodes ( head and neck, supraclavicular, axilla, infraclavicular, groin) in patients with cutaneous melanoma with or without sentinel lymph node biopsy (SLNB) or former elective or consecutive complete lymph node dissection in case of positive sentinel lymph node (CLND). Methods: Prospective multicenter study of the Departments of Dermatology of the Universities of Homburg/Saar, Tubingen and Munich (Germany) in which the distribution of lymph node and subcutaneous metastases were mapped from the scar of primary to the lymphatic drainage region in 53 melanoma patients ( 23 women, 30 men; median age: 64 years; median tumor thickness: 1.99 mm) with known primary, visible lymph nodes or subcutaneous metastases proven by ultrasound and histopathology during the follow-up. Results: Especially in the axilla, infraclavicular region and groin the metastases were not limited to the anatomic lymph node regions. In 5 patients (9.4%) ( 4 of them were in stage IV) lymph node metastases were not located in the corresponding lymph node area. 32 patients without former SLNB had a time range between melanoma excision and lymph node metastases of 31 months ( median), 21 patients with SLNB had 18 months ( p < 0.005). In 11 patients with positive SLNB the time range was 17 months, in 10 patients with negative SLNB 21 months ( p < 0.005); in 32 patients with CLND the time range was 31 m< 0.005). In thinner melanomas lymph node metastases occurred later ( p < 0.05). Conclusions: After surgery of cutaneous melanoma, SLNB and CLND the lymphatic drainage can show significant changes which should be considered in clinical and ultrasound follow-up examinations. Especially for high-risk melanoma patients follow-up examinations should be performed at intervals of 3 months in the first years. Patients at stage IV should be examined in all regional lymph node areas clinically and by ultrasound. Copyright (c) 2006 S. Karger AG, Basel

Gibbs' paradox and black-hole entropy

In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm of the particle number. We discuss here how analogous situations arise in the statistical foundation of black-hole entropy. Depending on the underlying approach to quantum gravity, the fundamental objects to be counted have to be assumed indistinguishable or not in order to arrive at the Bekenstein--Hawking entropy. We also show that the logarithmic corrections to this entropy, including their signs, can be understood along the lines of standard statistical mechanics. We illustrate the general concepts within the area quantization model of Bekenstein and Mukhanov.Comment: Contribution to Mashhoon festschrift, 13 pages, 4 figure