|dc.contributor.advisor||Del Debbio, Luigi||en
|dc.description.abstract||The energy-momentum tensor (EMT) is the Noether current associated with
translations. It is of interest because, first of all, it has physical meaning as it
contains the energy density and the momentum density. Moreover, its trace can
be related to the beta function so that the scaling behaviour of the theory at
hand can be studied. We are particularly interested in the scaling behaviour of
strongly coupled theories. To explore the strong coupling regime it is necessary
to compute the EMT non-perturbatively, i.e. on the lattice. This complicates
matters greatly. On the lattice translation invariance is broken which leads to
additional terms in the translation Ward identity from which the EMT is derived.
This results in turn in the need to renormalise the EMT on the lattice.
In this thesis we extend recent studies on the renormalisation of the EMT
in four-dimensional gauge theory to the case of a three-dimensional scalar
theory to investigate its divergence structure and the numerical feasibility of the
suggested procedure on a more basic level. Furthermore, scalar φ4-theory in three
dimensions exhibits an infrared fixed point and can thus serve as a toy model to
examine mechanisms for building theories beyond the standard model.
Our strategy to renormalise the EMT on the lattice is to identify all possible terms
that can mix with both sides of the translation Ward identity. The renormalised
EMT is a combination of operators of the same or lower dimension obeying
the symmetries of the theory. The mixing is determined by requiring that the
renormalised EMT satisfies the correct Ward identities. Using different probes
in the translation Ward identity one can compute the coefficients of the EMT
by solving a linear system of equations. However, contact terms can arise. One
solution is the recently introduced Wilson flow. Its renormalisation properties allow for expectation values free of contact terms. That way the Wilson flow provides for a meaningful theoretical formulation of the EMT on the lattice that can be used in practice.
In this thesis we review the renormalisation properties and the phase diagram
of scalar φ4-theory in three dimensions, the translation Ward identity and the
EMT in the continuum, as well as the gradient flow for scalar theory. A large
part is dedicated to the perturbative renormalisation of the EMT on the lattice.
Finally, our strategy to compute the renormalisation constants of the EMT in
scalar theory non-perturbatively is discussed in detail, and our results for the
renormalisation constants are presented.||en
|dc.contributor.sponsor||Science and Technology Facilities Council (STFC)||en
|dc.publisher||The University of Edinburgh||en
|dc.relation.hasversion||F. Capponi, A. Rago, L. Del Debbio, S. Ehret, and R. Pellegrini. Renormalisation of the energy-momentum tensor in scalar field theory using the Wilson ow. PoS, LATTICE2015:306, 2016.||en
|dc.relation.hasversion||F. Capponi, L. Del Debbio, S. Ehret, R. Pellegrini, A. Portelli, and A. Rago. Renormalisation of the scalar energy-momentum tensor with the Wilson flow. PoS, LATTICE2016:341, 2016.||en
|dc.title||Energy-momentum tensor from Wilson flow in lattice φ4-theory||en
|dc.type||Thesis or Dissertation||en
|dc.type.qualificationname||PhD Doctor of Philosophy||en