This dissertation is a synthesis of work completed during my Ph.D., loosely connected by the appearance of higher spin particles.

In Chapter 2, we explicitly construct an affine generalization of the Dirac action employing infinite dimensional spinorial representations of the group. This implies that it is built from an infinite number of spinor Lorentz multiplets with all possible half integer spins. We introduce a systematic procedure for constructing $GL(d,\mathbb{R})$ and $SL(d,\mathbb{R})$ invariant interaction terms to obtain quite general interacting models. Such models have order operators whose expectation value can break affine symmetry to Poincar {e} symmetry. This symmetry breaking pattern is known to exhibit a graviton as its Goldstone boson. We discuss possible interactions and mechanisms for this symmetry breaking to occur, which would provide a dynamical explanation of the Lorentzian signature of spacetime.

In Chapter 3, we study consistent deformations of Veneziano and Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.

In Chapter 4, we construct a new formalism for free massive particles of any spin, including integers and half integers, in any spacetime dimension. Massive particles are realized in this formalism as ``dimensionally reduced" massless particles. Explicit propagators are found for any spin and dimension, including the propagators for all auxiliary fields necessary in the formalism. For spin $s=n,n+1/2$, the propagators may be expressed as degree $n$ Gegenbauer polynomials, whose asymptotic $n\to\infty$ properties are known. This enables one to take an appropriate classical limit for particles with classically relevant spin $S\sim \hbar n\gg\hbar$ without extrapolation, all while using dimensional regularization.