In recent work, R. Moerman and H. Weigert have introduced a truncation scheme for the Balitsky hierarchy, arguing that this is the most general possible method for obtaining finite Nc approximate solutions to the JIMWLK equation, while ensuring that these solutions obey several key properties that are known to be true of any exact solution to JIMWLK [1]. To carry out this truncation, it becomes necessary to systematically construct an orthogonal basis for the space of color singlets with purely adjoint indices. The primary contribution of this dissertation is to construct a basis that makes significant strides towards this goal, using irreducible representations of the permutation group Sk and recently-developed Hermitian Young projection operators [2–4]. Our method directly produces the basis for these singlets, avoiding the need to construct a basis for all multiplets and project out the singlets, as is common in other approaches. In our basis, orthogonality holds both between elements associated with non-isomorphic and isomorphic representations, with the exception of representations that are identical (and not just isomorphic). In working through the robust mathematical framework that describes this construction, we show that failures of orthogonality are a direct result of these basis elements being associated with identical induced representations arising from derangements with differing cycle structure, which suggests a possible strategy for constructing a fully-orthogonal basis in future research. We also prove that this basis always consists of elements that are real or purely imaginary and show how to determine these properties at the level of representations using characters and Frobenius reciprocity. We then shift gears to prove a small number of analytic properties of the images of commonly-used Wilson line operators. Explicitly, we provide a proof that hasn’t existed in the literature previously that the image of the dipole operator in the complex plane is the hypocycloid with Nc-cusps and we prove that all Wilson line operators that appear in the amplitude matrix used in the JIMWLK evolution of two quark-antiquark pairs are bounded by the unit circle.

Includes abstract. / Includes bibliographical references (p. 47-48). / The renormalizable Abelian quantum field theory model of Kroll, Lee and Zumino is used to calculate next-to-leading order corrections to the pion electromagnetic form factor in vector meson dominance. At zero temperature the predictions for both the form factor and electromagnetic radius are found to improve greatly over the tree level result, and are in good agreement with the experimental data. A calculation of the vertex and self energy functions in the Matsubara formalism at finite temperature do not agree with the results of the Gale & Kapusta calculations. The resulting prediction for the radius is found to increase with temperature, consistent vith ideas about haclronic deconfinernent.

Includes bibliographical references. / The greatest obstacle in calculating the self-energy Feynman diagram is that it is, in principle, linearly divergent. So far the self-energy of a massive quark in cavity quantum chromodynamics has only been calculated for the lowest cavity mode ls1/2. The methods used so far, have been based on the multiple reflection formalism, in which the zero reflection term is extracted out analytically and evaluated separately using Pauli-Villars regularization. This thesis is based on the dimensional regularization scheme, adapted for use in the cavity, by Stoddart et al., who calculated the self-energy for a massless quark. This involves analytically isolating the divergences using dimensional regularization and then removing the divergences using the minimal subtraction (ms) scheme or some similar subtraction scheme. In this thesis, the self-energies of massive quarks have been calculated using the ms scheme for a number of low-lying cavity modes. The ls1/2 results have also been compared with the Pauli-Villars regularization scheme used by Goldhaber, Jaffe and Hansson.

Bibliography: pages 141-143. / The direct reactions of pions with nuclei in the energy region of the πN(3,3) resonance are examined in the eikonal formalism. In particular, the angular and energy dependence of the elastic scattering of πsup(+-) from the calcium isotopes 40Ca, 48Ca is studied, using a detailed phenomenological approach. Excellent agreement is obtained with experimental data. A closely related investigation is also made of the inelastic excitation of low-lying collective states of 40Ca, 48Ca by pions. The resulting one-parameter fits yield deformation lengths which are compared with simple collective model predictions. The total cross-sections for neutral pion scattering from 40Ca, 48Ca in the resonance region are investigated as well, and predictions are made

Typical energy loss calcuations in AdS/CFT simulations use an initial condition of off-shell pairs of quarks placed back-to-back in the QGP, but a precise and theoretically motivated description of configuration does not exist. Quark virtuality can have noticeable effects on the rate of energy loss so a first principles calculation is needed for the early time behaviour of virtual particles soon after production. We use the Schwinger Keldysh formalism to calculate a perturbative expression for the Energy Momentum Tensor of hard partons created before the formation of the Quark Gluon Plasma. We propose this as a foundational model to use as an initial condition in jet energy loss calculations.

The colour glass condensate captures quantum chromodynamics in its application to high-energy collider experiments in the spirit of an effective field theory. In deeply inelastic lepton-hadron scattering experiments, as well as in hadron-hadron collisions, the internal degrees of freedom of in-state hadrons are dominated by a dense medium of gluonic matter called the colour glass condensate. Interactions with this medium by some (dilute) probe are most naturally described in terms of Wilson-lines and their correlators. The energy-dependence of these correlators is given by the JIMWLK (Jalilian-Marian+Iancu+McLerran+Weigert+Leonidov+Kovner) equa- tion which, when applied to a correlator, generates an infinite tower of coupled Dyson-Schwinger- like equations referred to as a Balitsky Hierarchy. In this thesis, I present a novel method for truncating, in a gauge-invariant and symmetry- preserving manner, the Balitsky hierarchy associated with matrices of Wilson-line correlators. This truncation is realized by parameterizing the energy-dependence of the symmetric and anti- symmetric parts of these matrices independently via energy-evolution operators which evolve ini- tial conditions in a manner akin to the time-evolution of Hermitian operators in the Heisenberg picture of quantum mechanics. These energy-evolution operators are path-ordered exponentials whose exponents are expanded in terms of energy-dependent "colour structure functions". I show how the properties of contributions to the expansion of these exponents (at each order in the expansion) are constrained by the group theory of SU(Nc).

We study the multiple radiative gluon emission off a massless and highly energetic quark in the pQCD picture. We introduce the Maximally Helicity Violating (MHV) techniques to cope with the complexities in computing cross sections in multi-jet QCD. The multiphoton emission in QED is reviewed to emphasize the efficiency of the MHV approach. We show that the computation of the multiple photon emission current provides insight into the understanding of the multiple radiative gluon emission in QCD. We then compute the momentum distribution for one, two and three soft and collinear radiative gluons from a hard struck quark. Our MHV results exhibit non-Abelian information about the correlation of gluons. As a phenomenological analysis, we study the energy spectrum for emitting radiative gluons using our MHV results. By comparing the MHV and the standard Poisson approximation of uncorrelated multiple emission results, we see that there is significant difference between the two methods.

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This thesis presents a series of results relating to conserved charges in general relativity. In particular, we give a general expression for a gravitational charge corresponding to a boost Killing vector. Further, we use Hamiltonian perturbative techniques to obtain generalizations of the first law of black hole mechanics pertaining to accelerated black holes, stationary Kaluza-Klein black holes and static Kaluza-Klein bubble spacetimes. Finally, we present a generalized Hamiltonian formulation of gravity adapted to a higher dimension splitting of spacetime, motivated by the physics of branes.