Associated scalar-vector production at the LHC within an effective Lagrangian approach

We consider the case in which a strong dynamics is responsible for Electro-Weak Symmetry Breaking (EWSB) and both a scalar $h$ and a vector $V$, respectively a singlet and a triplet under a custodial $SU\left(2\right)$, are relevant and have a mass below the cut-off $\Lambda\approx 4\pi v$. In this framework we study the total cross sections for the associated $Vh$ production at the LHC at 14 TeV as functions of two independent free parameters.Comment: To appear in the Proceedings of IFAE2010 - Incontri di Fisica delle Alte Energie, Rome, Italy, 7-9 April 201

Schrodinger representation for the polarized Gowdy model

The polarized ${\bf T}^3$ Gowdy model is, in a standard gauge, characterized by a point particle degree of freedom and a scalar field degree of freedom obeying a linear field equation on ${\bf R}\times{\bf S}^1$. The Fock representation of the scalar field has been well-studied. Here we construct the Schrodinger representation for the scalar field at a fixed value of the Gowdy time in terms of square-integrable functions on a space of distributional fields with a Gaussian probability measure. We show that ``typical'' field configurations are slightly more singular than square-integrable functions on the circle. For each time the corresponding Schrodinger representation is unitarily equivalent to the Fock representation, and hence all the Schrodinger representations are equivalent. However, the failure of unitary implementability of time evolution in this model manifests itself in the mutual singularity of the Gaussian measures at different times.Comment: 13 page

The Problems of Time and Observables: Some Recent Mathematical Results

We present 2 recent results on the problems of time and observables in canonical gravity. (1) We cannot use parametrized field theory to solve the problem of time because, strictly speaking, general relativity is not a parametrized field theory. (2) We show that there are essentially no local observables for vacuum spacetimes.Comment: Talk presented at the Lanczos Centenary Conference 3 pages, plain Te

A Deformation Theory of Self-Dual Einstein Spaces

The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local properties of the moduli space of self-dual Einstein connections are described in the context of an elliptic complex which arises in the linearization of the quadratic equations on the $SU(2)$ curvature. In particular, it is shown that the moduli space is discrete when the cosmological constant is positive; when the cosmological constant is negative the moduli space can be a manifold the dimension of which is controlled by the Atiyah-Singer index theorem.Comment: 13 page

Covariant Phase Space Formulation of Parametrized Field Theories

Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical (pre)symplectic structure. Motivated by issues arising in general relativity, we focus on: phase space representations of the spacetime diffeomorphism group, construction of observables, and the relationship between the canonical and covariant phase spaces.Comment: 22 page

Natural Symmetries of the Yang-Mills Equations

We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang-Mills connections we introduce a spinorial coordinate system that is adapted to the solution subspace defined by the Yang-Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a straightforward manner. We find that all natural symmetries of the Yang-Mills equations stem from the gauge transformations admitted by the equations.Comment: 23 pages, plain Te

Socially Optimal Criminal Justice System Waiting Times: A More General Theoretical Analysis

Criminal justice system delay, which is defined as the time elapsing between the defendant being charged and the case being listed at court, has up to some point, socially valuable flexibility value. This insight borrowed from the options literature in finance, makes it potentially possible to formally model and estimate socially optimal criminal justice system waiting times. This exercise is attempted in this paper by randomising the defendant’s probability of conviction, which is a critical argument in the defendant’s expected cost of going to trial and the monetary value of a conviction to society .The probability of conviction is assumed to conform to a uniform probability distribution with increasing variability until the trial date. What drives this variability is a continuous stream of information impacting on the defendant’s probability of conviction, which is continuously evaluated by the defendant and prosecutor as they formulate their different strategies given their respective conflicting objectives. Endogenising the probability of conviction in this way enables the respective payoffs of the defendant and prosecutor to be expressed as dynamic net present values per unit of time. The economic value of this flexibility to wait is measured as the rate of change in the sum of these dynamic NPVs per unit of time. Socially optimal delay is defined as the trial wait, which maximises the dollar value of the sum of the economic value of flexibility to the prosecutor (society) and the defendant simultaneously, and is the optimal time to list the case at the court. The corresponding dollar value is the total marginal social value of delay. Corresponding to the socially optimal wait and the total marginal social value of delay will be the optimal sentence discount for the prosecutor (society) to offer the defendant and the defendant’s optimal plea. Society makes a trade off between two conflicting objectives, the need to ensure justice to the defendant as legally and morally defined with the need to resolve the issue as quickly as possible.