Magnetic calculus and semiclassical trace formulas

The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the expansion of the trace of a function of the magnetic Schr\"odinger operator whose existence was established in \cite{HR2}

Hamiltonian reductions of free particles under polar actions of compact Lie groups

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.Comment: 15 pages, minor correction and updated references in v

Electromagnetism in terms of quantum measurements

We consider the question whether electromagnetism can be derived from quantum physics of measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way we justify the use of von Neumann-type measurement models for physical processes. We apply operational quantum measurement theory to gain insight in fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator deformations. In this way one can obtain quantized electromagnetism as a measurement of a system by another. The relevant deformations (Rieffel deformations) have a mathematically well-defined "classical" limit which is indeed classical electromagnetism for our choice of interaction

Quantum mechanics is about quantum information

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein's special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.Comment: 17 pages, forthcoming in Foundations of Physics Festschrift issue for James Cushing. Revised version: some paragraphs have been added to the final section clarifying the argument, and various minor clarifying remarks have been added throughout the tex

Disease extinction in the presence of non-Gaussian noise

We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations. We show that, in the absence of vaccinations, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.Comment: Accepted for publication to PR

Shear viscosity in ϕ4\phi^4 theory from an extended ladder resummation

We study shear viscosity in weakly coupled hot $\phi^4$ theory using the CTP formalism . We show that the viscosity can be obtained as the integral of a three-point function. Non-perturbative corrections to the bare one-loop result can be obtained by solving a decoupled Schwinger-Dyson type integral equation for this vertex. This integral equation represents the resummation of an infinite series of ladder diagrams which contribute to the leading order result. It can be shown that this integral equation has exactly the same form as the Boltzmann equation. We show that the integral equation for the viscosity can be reexpressed by writing the vertex as a combination of polarization tensors. An expression for this polarization tensor can be obtained by solving another Schwinger-Dyson type integral equation. This procedure results in an expression for the viscosity that represents a non-perturbative resummation of contributions to the viscosity which includes certain non-ladder graphs, as well as the usual ladders. We discuss the motivation for this resummation. We show that these resummations can also be obtained by writing the viscosity as an integral equation involving a single four-point function. Finally, we show that when the viscosity is expressed in terms of a four-point function, it is possible to further extend the set of graphs included in the resummation by treating vertex and propagator corrections self-consistently. We discuss the significance of such a self-consistent resummation and show that the integral equation contains cancellations between vertex and propagator corrections.Comment: Revtex 40 pages with 29 figures, version to appear in Phys. Rev.

Analytic and Numerical Study of Preheating Dynamics

We analyze the phenomenon of preheating,i.e. explosive particle production due to parametric amplification of quantum fluctuations in the unbroken case, or spinodal instabilities in the broken phase, using the Minkowski space $O(N)$ vector model in the large $N$ limit to study the non-perturbative issues involved. We give analytic results for weak couplings and times short compared to the time at which the fluctuations become of the same order as the tree level,as well as numerical results including the full backreaction.In the case where the symmetry is unbroken, the analytic results agree spectacularly well with the numerical ones in their common domain of validity. In the broken symmetry case, slow roll initial conditions from the unstable minimum at the origin, give rise to a new and unexpected phenomenon: the dynamical relaxation of the vacuum energy.That is, particles are abundantly produced at the expense of the quantum vacuum energy while the zero mode comes back to almost its initial value.In both cases we obtain analytically and numerically the equation of state which turns to be written in terms of an effective polytropic index that interpolates between vacuum and radiation-like domination. We find that simplified analysis based on harmonic behavior of the zero mode, giving rise to a Mathieu equation forthe non-zero modes miss important physics. Furthermore, analysis that do not include the full backreaction do not conserve energy, resulting in unbound particle production. Our results do not support the recent claim of symmetry restoration by non-equilibrium fluctuations.Finally estimates of the reheating temperature are given,as well as a discussion of the inconsistency of a kinetic approach to thermalization when a non-perturbatively large number of particles is created.Comment: Latex file, 52 pages and 24 figures in .ps files. Minor changes. To appear in Physical Review D, 15 December 199

Out of equilibrium O (N) linear-sigma system - Construction of perturbation theory with gap- and Boltzmann-equations

We establish from first principles a perturbative framework that allows us to compute reaction rates for processes taking place in nonequilibrium $O (N)$ linear-sigma systems in broken phase. The system of our concern is quasiuniform system near equilibrium or nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. No further approximation is introduced. In the course of construction of the framework, we obtain the gap equation that determines the effective masses of $\pi$ and of $\sigma$, and the generalized Boltzmann equation that describes the evolution of the number-density functions of $\pi$ and of $\sigma$.Comment: 18 page

Group Averaging for de Sitter free fields

Perturbative gravity about global de Sitter space is subject to linearization-stability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity {\it only} if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitter-invariant states except the vacuum, though a new Hilbert space of de Sitter invariant states can be constructed via so-called group-averaging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general $N$-particle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.Comment: 33 pages, 2 figure

Temperature dependence of the anomalous effective action of fermions in two and four dimensions

The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four dimensions. The calculation preserves chiral symmetry and confirms that a temperature dependence is compatible with axial anomaly saturation. The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.Comment: RevTex, 19 pages, no figures. References adde