Characterizations of the solution sets of pseudoinvex programs and variational inequalities

Author name used in this publication: Heungwing Lee2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Ghost and tachyon free gauge theories of gravity: A systematic approach

In this thesis, we present a systematic method for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity about a Minkowski background for it to be free of ghost or tachyon particles. The approach naturally accommodates critical cases in which the parameter values satisfying some critical conditions causing changes of particle contents and may lead to additional gauge invariances. In Chapter 1, we give an overall introduction to the field. We then introduce the systematic method in Chapter 2. The method is implemented as a computer program, and the details of its implementation are presented in Chapter 3. In Chapter 4, we apply the method to investigate the particle content of parity-conserving Poincar\'e gauge theory (PGT$^+$). We find 450 critical cases that are free of ghosts and tachyons and compare the no-ghost-and-tachyon conditions of some critical cases with literature. We also examine the power-counting renormalisability of some of the critical cases of PGT$^+$ and clarify the treatment of non-propagating modes in determining whether a theory is power-counting renormalisable (PCR) in Chapter 5. We identify 58 of the ghost and tachyon free PGT$^+$ critical cases that are also PCR, of which seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, 12 have only 2 massless d.o.f., and 39 have only massive mode(s). In chapter 6, we analyse parity-preserving Weyl gauge theory (WGT$^+$) in a similar way. Within a subset of WGT$^+$, we find 168 critical cases that are free of ghosts and tachyons. We further identify 40 of these cases that are also PCR. Of these theories, 11 have only massless tordion propagating particles, 23 have only a massive tordion propagating mode, and 6 have both. We also repeat our analysis for PGT$^+$ and WGT$^+$ with vanishing torsion or curvature, respectively. In Chapter 7, we summarise the contents in this thesis and suggest some future work