School of MathematicsSchool of Mathematicshttp://hdl.handle.net/2262/12017-01-19T10:55:24Z2017-01-19T10:55:24ZThe radiation bound for a Klein-Gordon field on a static spherical spacetimeCollins, Michael Patrickhttp://hdl.handle.net/2262/788472017-01-19T03:16:21Z2013-01-01T00:00:00ZThe radiation bound for a Klein-Gordon field on a static spherical spacetime
Collins, Michael Patrick
We establish a well-posed Cauchy problem in Minkowski (R4, η), associated with a radiating Klein-Gordon field ψ(x) = eztψ(xi), in curvature coordinates {xμ = t, p, θ,Φ} on a static spherically symmetric spacetime (M, g). This is crucial to our primary concern with proving an optimal L2-bound on the radiating field ψ, decaying at asymptotic spatial infinity, and manifests as the content of our main Theorem 1: A proof of the Sommerfeld Finiteness Condition for K-G radiation on (M,g).
2013-01-01T00:00:00ZCR Singularities in condimension 2Burcea, Valentin Danielhttp://hdl.handle.net/2262/788312017-01-19T03:14:03Z2013-01-01T00:00:00ZCR Singularities in condimension 2
Burcea, Valentin Daniel
In this thesis we study the real submanifolds of codimension 2 in a complex manifold near a CR singularity. The thesis has 3 chapters. In Chapter 1 we shall make a small introduction where we will remind some basic notions and known results. The first chapter has 3 parts. In the first part we recall some basic notions. The second part represents an preparation for the second chapter. The third part represent a preparation for the third chapter. The main result of the thesis represent the content of Chaper 2. We generalize to a higher dimensional case Huang-Yin’s normal form in C2. The main tool is given by the Fisher decomposition and our construction is done following the lines of Huang-Yin’s normal form construction.
The last Chapter contains some remarks about a family of analytic discs attached to a real submanifold and some applications.
2013-01-01T00:00:00ZFree Field Representation and Form Factors of the Chiral Gross-Neveu ModelBritton, Stephenhttp://hdl.handle.net/2262/788242017-01-19T03:11:17Z2013-01-01T00:00:00ZFree Field Representation and Form Factors of the Chiral Gross-Neveu Model
Britton, Stephen
The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.
2013-01-01T00:00:00ZSymanzik Iimprovement of the gradient flow in lattice gauge theoriesSINT, STEFANhttp://hdl.handle.net/2262/787272017-01-14T03:01:51Z2015-01-01T00:00:00ZSymanzik Iimprovement of the gradient flow in lattice gauge theories
SINT, STEFAN
We apply the Symanzik improvement progra-
mme to the 4
+
1-dimensional local re-formulation of the
gradient flow in pure
SU
(
N
)
lattice gauge theories. We show
that the classical nature of the flow equation allows one to
eliminate all cutoff effects at
O
(
a
2
)
, which originate either
from the discretised gradient flow equation or from the gradi-
ent flow observable. All the remaining
O
(
a
2
)
effects can be
understood in terms of local counterterms at the zero flow-
time boundary. We classify these counterterms and provide
a complete set as required for on-shell improvement. Com-
pared to the 4-dimensional pure gauge theory only a single
additional counterterm is required, which corresponds to a
modified initial condition for the flow equation. A consis-
tency test in perturbation theory is passed and allows one to
determine all counterterm coefficients to lowest non-trivial
order in the coupling.
PUBLISHED
2015-01-01T00:00:00Z