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We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws related to Poincare invariance within the different approaches. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.
We give the exact solution of classical equation of motion of a quartic scalar massless field theory showing that this is massive and is represented by a superposition of free particle solutions with a discrete spectrum. Then we show that this is als
A spinless covariant field $phi$ on Minkowski spacetime $M^{d+1}$ obeys the relation $U(a,Lambda)phi(x)U(a,Lambda)^{-1}=phi(Lambda x+a)$ where $(a,Lambda)$ is an element of the Poincare group $Pg$ and $U:(a,Lambda)to U(a,Lambda)$ is its unitary repre
Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Greens functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional
We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits both Lagr
We review the covariant canonical formalism initiated by DAdda, Nelson and Regge in 1985, and extend it to include a definition of form-Poisson brackets (FPB) for geometric theories coupled to $p$-forms, gauging free differential algebras. The form-L