62 research outputs found

    Why is Schrodinger's Equation Linear?

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    Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear corrections to quantum theory. Nonlinear corrections can also appear in a Lorentz invariant theory in the form of higher derivative terms that are determined by a length scale, possibly the Planck length. It is suggested that the best place to look for evidence of such quantum nonlinear effects is in neutrino physics and cosmology.Comment: 3 pages; Presented at the DICE 2004 workshop; Sept 2004, Piombino Italy. Minor corrections: this is the proceedings Versio

    Nonlinear Dirac Equations

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    We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations

    An Approximate Expression for the Large Angle Period of a Simple Pendulum

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    A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.Comment: 6 page

    The Pressure of Hot g2ϕ4g^2 \phi^4 Theory at order g5g^5

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    The order g5g^5 contribution to the pressure of massless g2ϕ4g^2 \phi^4 theory at nonzero temperature is obtained explicitly. Lower order contributions are reconsidered and two issues leading to the optimal choice of rearranged Lagrangian for such calculations are clarified.Comment: 15 pages, Latex, postscript file attached at the en