There is almost universal agreement among astronomers that most of the mass in the Universe and most of the mass in the Galactic halo is dark. Many lines of reasoning suggest that the dark matter consists of some new, as yet undiscovered, weakly-interacting massive particle (WIMP). There is now a vast experimental effort being surmounted to detect WIMPS in the halo. The most promising techniques involve direct detection in low-background laboratory detectors and indirect detection through observation of energetic neutrinos from annihilation of WIMPs that have accumulated in the Sun and/or the Earth. Of the many WIMP candidates, perhaps the best motivated and certainly the most theoretically developed is the neutralino, the lightest superpartner in many supersymmetric theories. We review the minimal supersymmetric extension of the Standard Model and discuss prospects for detection of neutralino dark matter. We review in detail how to calculate the cosmological abundance of the neutralino and the event rates for both direct- and indirect-detection schemes, and we discuss astrophysical and laboratory constraints on supersymmetric models. We isolate and clarify the uncertainties from particle physics, nuclear physics, and astrophysics that enter at each step in the calculation. We briefly review other related dark-matter candidates and detection techniques.

Supersymmetric Dark Matter

Gravitation, Gauge Theories and Differential Geometry

The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

http://wonka.physics.ncsu.edu/~tmschaef/physics/RevModPhys_Instantons.pdf

Instantons in QCD

Phase transitions in Abelian lattice gauge theories

A new classical solution of the Yang-Mills field equations

This paper describes a functional formulation of Euclidean quantum field theory, based on a complete equivalence with classical statistical mechanics. One introduces an extra time variable and sets up a canonical scheme with new Lagrangian and Hamiltonian functions. The generating functional is then defined as the Gibbs average over the ensemble. This allows us, in particular, to control in a simple way the invariance properties of the integration measure. In several cases of physical interest it is seen that the invariance requirement leads to extra determinantal factors in the integration volume and, therefore, to a set of improved Feynman rules. In particular, enforcing dilatation invariance for the generating functional is shown to lead to a nonzero background,i.e. to spontaneous breaking of the symmetry. The application of the method to constrained systems is discussed in detail and in the case of Yang-Mills theories the Faddeev-Popov prescription for quantization is reproduced with remarkable simplicity. A discussion of the functional quantization of gravity is also offered.

/pdf/on-the-functional-formulation-of-quantum-field-theory-1k83koiisk.pdf

On the functional formulation of quantum field theory

In this paper the analytic properties of the fixed angular momentum amplitudes of the deuteron photodisintegration are investigated by a potential model. It is shown that these properties agree with those obtained by a Mandelstam representation with anomalous thresholds, as argued by perturbation arguments. This is an argument in favour of the validity of general dispersion techniques also in nuclear physics.

Potential model of deuteron photodisintegration and Mandelstam representation

Direct search for neutralino dark matter is analyzed in the framework of the minimal supersymmetric extension of the standard model, using a realistic evaluation of the neutralino relic abundance which also includes radiative corrections to the Higgs masses Relevance of the present (Ge detectors) experimental data to set constraints on the parameters of the model is discussed and expectations for future experiments which involve neutralino-nucleus coherent processes are investigated These results are compared to those obtained in a previous paper from indirect search data In the present analysis particular attention is paid to the theoretical uncertainties due to the different estimates of the Higgs-nucleon coupling strength

Direct versus indirect searches for neutralino dark matter

We review classical solutions, both of the instanton and meron type, for the nonlinear σ-model in two dimensions and discuss their generalization to the four-dimensional case, which involves a fourth-order derivative Lagrangian.

V. De Alfaro

Papers

A new classical solution of the Yang-Mills field equations

On the functional formulation of quantum field theory

Potential model of deuteron photodisintegration and Mandelstam representation

Direct versus indirect searches for neutralino dark matter

Nonlinear σ-models and classical solutions