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We present a new formula for the gauge charge in the causal formalism for the QCD case., Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:2007.01115; text overlap with arXiv:1612.04998

It is known that the elimination of the anomalies in all orders of perturbation theory is an open problem. The constrains given by usual invariance properties and the Wess-Zumino identities are not enough to eliminate the anomalies in the general case of an Yang-Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of the perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of the perturbation theory. So, anti-BRST transform gives nothing new, and we have to find other ideas to restrict and eventually eliminate the anomalies for a general Yang-Mills theory., Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:1301.3664, arXiv:1301.2893, arXiv:1403.4472, arXiv:0711.3986

We present a coordinate space version of the factorization formula for the connected tree part of the chronological products. We consider a general framework and then we apply it for the QCD case., Comment: 24 pages. arXiv admin note: text overlap with arXiv:1612.04998

The tensor Feynman amplitudes are reduced to scalar integrals by a procedure of Passarino and Veltman. We provide an alternative approach based on the causal formalism., Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1910.10640

The gauge invariance of some massless Yang-Mills models can be proved for a large class of groups using Polchinski flow equations approach. In this paper we provide an alternative proof based on the causal approach. The proof is purely algebraic and is based on the analysis of the anomalies. More precisely, one can prove that the anomalies are verifying some consistency equations of Wess-Zumino type. In the massless SU(2) Yang-Mills case, this is enough to prove that they are absent. The same is true for QED., Comment: 29 pages, Contribution to the conference "Quantum Fields and Nonlinear Phenomena" 18-22 April 2018, Sinaia, Romania

We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study massive gravity which is not trivial. In the limit of vanishing graviton mass we obtain a non-trivial massless theory different from Einstein gravity. We derive the interaction from descent equations and obtain the cosmological topologically massive gravity. However, in addition to Einstein and Chern-Simons coupling we need coupling to fermionic ghost and anti-ghost fields and to a vector-graviton field with the same mass as the graviton., Comment: 15 pages

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 pages

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity., Comment: 12 pages, no figure

We determine the most general form of the interaction between the gravitational field and an arbitrary Yang-Mills system of fields (massless and massive). We work in the perturbative quantum framework of the causal approach (of Epstein and Glaser) and use a cohomological definition of gauge invariance for both gauge fields. We also consider the case of massive gravity. We discuss the question whether gravity couples to the unphysical degrees of freedom in the Yang-Mills fields., Comment: no figures, 13 pages

Quantum theory of the gauge models in the causal approach leads to some cohomology problems. We investigate these problems in detail., Comment: 57 pages, no figures

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 figure

Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the second order derivatives. This structure can be used to make more precise the form of a general symmetry. As an illustration we analyse the case of Lagrangian equations with Poincar\'e invariance or with universal invariance., Comment: 21 pages, LATEX

A general discussion of the construction of free fields based on Weinberg anszatz is provided and various applications appearing in the litterature are considered., Comment: 10 pages, IFA-FT-400, LATEX

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, April

A complete list of all transitive symplectic manifolds of the Poincar\'e and Galilei group in 1+2 dimensions is given., Comment: LATEX, #15 pages, IFA-FT-392-1994, January

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, December

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-TEX