Resummation in a Hot Scalar Field Theory

A resummed perturbative expansion is used to obtain the self-energy in the high-temperature $g^2\phi^4$ field theory model up to order $g^4$. From this the zero momentum pole of the effective propagator is evaluated to determine the induced thermal mass and damping rate for the bosons in the plasma to order $g^3$. The calculations are performed in the imaginary time formalism and a simple diagrammatic analysis is used to identify the relevant diagrams at each order. Results are compared with similar real-time calculations found in the literature.Comment: 26 pages (figures not included

Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.Comment: Final proceedings version. 6 pages. Presented at the 3rd QTRF conference at Vaxjo, Sweden, June6-11 200

Why is Schrodinger's Equation Linear?

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

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

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component ϕ4\phi^4 theory

Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.Comment: 16pages, Latex, typographical errors are correcte