Search results for "Mathematica"
showing 10 items of 7971 documents
Inflation, quantum fields, and CMB anisotropies
2009
Revert field Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions.
Geometry of the theory space in the exact renormalization group formalism
2018
We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
2002
Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…
Considerations concerning the renormalization of the electroweak sector of the standard model
1990
Abstract Examination of the structure of one-loop corrected amplitudes for arbitrary processes mediated by W, Z and γ in the simple renormalization framework previously discussed by the author, leads to natural choices for the renormalized self-energies and vertex corrections. They satisfy simple renormalization conditions and, as q2 → 0, the W and Z propagators approach the free expressions with a correction of O(αq2/mW2). The renormalization conditions allow us to circumvent certain ambiguities that arise, to O(α2), in current analyses of Δr and κ(q2). A useful simplified form for the Z propagator is presented.
Non-perturbative renormalization in kaon decays
1996
We discuss the application of the MPSTV non-perturbative method \cite{NPM} to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the $\Delta I=1/2$ rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the $B_K$ parameter.
Beyond the triangle and uniqueness relations: non-zeta counterterms at large $N$ from positive knots
1997
Counterterms that are not reducible to ζn are generated by 3F2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N 3) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Pade resummations of e-expansions, which are compared with analytical results in 3 dimensions. The O(1/N 3) results entail knots gener…
Perturbative quantum field theory
2000
pQFT In this chapter we repeat the main steps towards a derivation of the Feynman rules, following the well-known path of canonical quantization. This is standard material, and readers who are not acquainted with such topics are referred to [Bjorken and Drell 1965, Bogoliubov and Shirkov 1980, Itzykson and Zuber 1980, Kaku 1993, Weinberg 1995, Peskin and Schroeder 1995, Teller 1997]. We hope that the short summary given here, similar to that in [Kreimer 1997a], is helpful for readers who want to refresh their memory. Having introduced Feynman rules, we next introduce Schwinger–Dyson equations as a motivation for the introduction of Z -factors. We remark on dimensional regularization and giv…
Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data
2008
Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.
A simple method for measurement of mechanical power in jumping.
1983
A simple test for the measurement of mechanical power during a vertical rebound jump series has been devised. The test consists of measuring the flight time with a digital timer (+/- 0.001 s) and counting the number of jumps performed during a certain period of time (e.g., 15-60 s). Formulae for calculation of mechanical power from the measured parameters were derived. The relationship between this mechanical power and a modification of the Wingate test (r = 0.87, n = 12 males) and 60 m dash (r = 0.84, n = 12 males) were very close. The mechanical power in a 60 s jumping test demonstrated higher values (20 W X kgBW-1) than the power in a modified (60 s) Wingate test (7 W X kgBW-1) and a Mar…
Scientific abstracts and plain language summaries in psychology: A comparison based on readability indices.
2020
Findings from psychological research are usually difficult to interpret for non-experts. Yet, non-experts resort to psychological findings to inform their decisions (e.g., whether to seek a psychotherapeutic treatment or not). Thus, the communication of psychological research to non-expert audiences has received increasing attention over the last years. Plain language summaries (PLS) are abstracts of peer-reviewed journal articles that aim to explain the rationale, methods, findings, and interpretation of a scientific study to non-expert audiences using non-technical language. Unlike media articles or other forms of accessible research summaries, PLS are usually written by the authors of th…