Conformal Invariance in Classical Field Theory

A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.Comment: 18 pages, PLAIN-TE

Free Fields for Any Spin in 1+2 Dimensions

We construct free fields of arbitrary spin in 1+2 dimensions i.e. free fields for which the one-particle Hilbert space carries a projective isometric irreducible representation of the Poincar\'e group in 1+2 dimensions. We analyse in detail these representations in the fiber bundle formalism and afterwards we apply Weinberg procedure to construct the free fields. Some comments concerning axiomatic field theory in 1+2 dimensions are also made.Comment: 33 pages, IFA-FT-394-1994, Apri

The Projective Unitary Irreducible Representations of the Galilei Group in 1+2 Dimensions

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of $G^{\uparrow}_{+}$.Comment: 15 pages, LATEX, preprint IFA-FT-391-1993, Decembe

Massive gravity from descent equations

Both massless and massive gravity are derived from descent equations (Wess-Zumino consistency conditions). The massive theory is a continuous deformation of the massless one.Comment: 8 pages, no figur

The Interaction of Quantum Gravity with Matter

The interaction of (linearized) gravitation with matter is studied in the causal approach up to the second order of perturbation theory. We consider the generic case and prove that gravitation is universal in the sense that the existence of the interaction with gravitation does not put new constraints on the Lagrangian for lower spin fields. We use the formalism of quantum off-shell fields which makes our computation more straightforward and simpler.Comment: 25 page

The Projective Unitary Irreducible Representations of the Poincar\'e Group in 1+2 Dimensions

We give a complete analysis of the projective unitary irreducible representations of the Poincar\'e group in 1+2 dimensions applying Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2 dimensions. We provide explicit formulae for all representations.Comment: 22 pages, PLAIN-TE