Pure & Applied MathematicsPure & Applied Mathematicshttp://hdl.handle.net/2262/592019-07-21T11:03:18Z2019-07-21T11:03:18ZOn the Symanzik improvement of gradient flow observablesRUBEO, ARGIAhttp://hdl.handle.net/2262/872652019-06-14T02:02:55Z2019-01-01T00:00:00ZOn the Symanzik improvement of gradient flow observables
RUBEO, ARGIA
The gradient flow provides a new class of renormalised observables which can be measured with high precision in lattice simulations. This is relevant for many interesting applications. However, such applications are made difficult by the large discretisation effects observed in many gradient flow observables. We refer to the pure gauge theory at O(g02) in perturbation theory, where the structure of the Symanzik effective theory and all counterterms are known. At this order in perturbation theory, the theoretical expectation is that O(a2) Symanzik improvement is achieved when the action, the observable and the flow are O(a2) improved. We compute numerically the simplest observable, i.e. the action density, both with SF and SF-open boundary conditions. The first outcome of our computation confirms the theoretical expectation about the O(a2) improvement. Then we analyse a set-up with unimproved action. In finite volume, we study if it is possible to improve the observables by tuning the coefficient in the initial condition for the flow. Our analysis shows that very different values of cb are needed depending on the specific observable we want to improve. We show that the hypothesis that there is a hierarchy of cutoff effects between flow and non-flow observables is not valid, therefore it is not possible to find a universal value for the coefficient related to the only counterterm needed with respect to the 4 dimensional theory.
APPROVED
2019-01-01T00:00:00ZA formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetryWatterson, Stevenhttp://hdl.handle.net/2262/866632019-05-03T02:16:22Z2008-01-01T00:00:00ZA formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry
Watterson, Steven
In this thesis, we develop the Geometric Discretization formulation of Dirac-Kahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that we can use the two complexes associated with the definition of the Hodge star to construct chiral projection operators that exactly project a different chirality of held on to each complex. Similarly, we construct flavour projection operators that project a different flavour of field on to each complex. We also see that, in two space-time dimensions, we need four complexes to simultaneously separate the chiral and flavour components of the field.
2008-01-01T00:00:00ZA theoretical study of spin filtering and its application to polarizing antiprotonsO'Brien, Domhnaillhttp://hdl.handle.net/2262/865532019-05-02T02:39:34Z2008-01-01T00:00:00ZA theoretical study of spin filtering and its application to polarizing antiprotons
O'Brien, Domhnaill
There has been much recent research into possible methods of polarizing an antiproton
beam, the most promising being spin filtering, the theoretical understanding of
which is currently incomplete. The method of polarization buildup by spin filtering
requires many of the beam particles to remain within the beam after repeated interaction
with an internal target in a storage ring. Hence small scattering angles,
where we show that electromagnetic effects dominate hadronic effects, are important.
All spin-averaged and spin-dependent electromagnetic cross-sections and spin
observables for elastic spin 1/2 - spin 1/2 scattering, for both point-like particles
and non-point-like particles with internal structure defined by electromagnetic form
factors, are derived to first order in QED. Particular attention is paid to spin transfer
and depolarization cross-sections in antiproton-proton, antiproton-electron and
positron-electron scattering, in the low |t| region of momentum transfer. A thorough
mathematical treatment of spin filtering is then presented, identifying the key
physical processes involved and highlighting the dynamical properties of the physical
system. We present and solve sets of differential equations which describe the
buildup of polarization by spin filtering in many different scenarios of interest. The
advantages of using a lepton target are outlined, and finally a proposal to polarize
antiprotons by spin filtering off an opposing polarized electron beam is investigated.
2008-01-01T00:00:00ZAnisotropic discretisations and practical all-to-all propagators for lattice QCDÓ Cais, Aileinhttp://hdl.handle.net/2262/865422019-05-02T02:36:26Z2006-01-01T00:00:00ZAnisotropic discretisations and practical all-to-all propagators for lattice QCD
Ó Cais, Ailein
In this thesis, we concern ourselves primarily with improving the accuracy of the determination of correlation functions in lattice QCD. We detail two avenues of improvement and implement them both, separately and in combination. Firstly, we formulate an improved anisotropic action which is classically correct to O(a3s,a2t). The employment of an anisotropic lattice introduces the anisotropy ratio, ξ = as/at, which we tune non-perturbatively. In a quenched lattice simulation, we find that the mass dependence of the tuning of this parameter is weak, and a single tuning suffices for a range of quark masses from the strange quark mass to well above charm quark mass. The primary benefit of an anisotropic action is that it allows us an increased number of lattice sites in the temporal direction with which to study the exponential decay of correlation functions.
2006-01-01T00:00:00Z