Quantum chromodynamics (QCD) is the modern theory of strong interactions. Quarks and antiquarks interact extit{via} gluons, the gauge bosons, and form well-know bound states, namely mesons and baryons. This non-Abelian gauge theory predicts the existence of unconventional states of quarks and gluons: Exotic hadrons. Their observation remains a difficult task since their properties are poorly known. Their theoretical study is a challenging task and will guide experimentalists in their work. This thesis is devoted to two main types of exotic hadrons: Hybrid mesons and glueballs. Hybrid mesons are mesons in which the gluon field is in an excited state. In constituent models, the excitation of the flux tube is interpreted in term of a constituent gluon. In this thesis, the connection between the two pictures, flux tube excitation and constituent gluon, is demonstrated. Using the technique of the auxiliary field, we reproduce, from the three-body system quark-antiquark-gluon, the excitations of the quark-antiquark potential observed in lattice QCD. We complete our study of mesons with exotic quantum numbers by performing a analysis of the low-lying spectrum. Glueballs are hadronic states with no valence quarks. Theoretical developments suggests that confined gluons gain a constituent mass inside glueballs. According to this, a gluon can be considered as a heavy spin-1 particle. Two- and three-gluon glueballs are then similar of heavy meson and baryon systems. We preformed a complete study of the low-lying spectrum of these glueballs. The comparison with the pure gauge results from lattice QCD showed a disagreement and led us to the conclusion that the gluon degree-of-freedom was not correctly taken into account. Indeed, the implementation of transverse gluons at the level of the wave functions solved this problem for two-gluon glueballs. For both systems, hybrid mesons and glueballs, we used semi-relativistic Hamiltonians since they remain valid for massless particles. A code in Gaussian basis was developed to solve our eigenvalue problems. For this purpose, we found the matrix elements between Gaussian functions for various operators.

Elementary particles form hadrons through the strong interaction; one interpretation of a possible hadron bound-state is a hybrid meson which is composed of a quark-antiquark pair and gluonic content. Non-exotic hybrid mesons share spin <i>J</i>, parity <i>P</i> and charge conjugation <i>C</i> quantum numbers with quark-antiquark states while exotic hybrids do not. Aspects of particle physics, strong interactions, and quantum field theory necessary for calculating the correlation function for a hybrid meson will be reviewed. In particular, the perturbative part of the correlation function for a hybrid meson with <i>J</i>^PC=1^-- will be formulated in terms of Feynman rules and diagrams and calculated to next-to-leading order in the light (massless) quark case. Assuming the hybrid current renormalizes multiplicative, the next-to-leading order effects are found to be large, and are potentially important for future determinations of the light-quark non-exotic hybrid meson.

Elementary particles form hadrons through the strong interaction; one interpretation of a possible hadron bound-state is a hybrid meson which is composed of a quark-antiquark pair and gluonic content. Non-exotic hybrid mesons share spin <i>J</i>, parity <i>P</i> and charge conjugation <i>C</i> quantum numbers with quark-antiquark states while exotic hybrids do not. Aspects of particle physics, strong interactions, and quantum field theory necessary for calculating the correlation function for a hybrid meson will be reviewed. In particular, the perturbative part of the correlation function for a hybrid meson with <i>J</i>^PC=1^-- will be formulated in terms of Feynman rules and diagrams and calculated to next-to-leading order in the light (massless) quark case. Assuming the hybrid current renormalizes multiplicative, the next-to-leading order effects are found to be large, and are potentially important for future determinations of the light-quark non-exotic hybrid meson.