Spacetime locality in Sp(2) symmetric lagrangian formalism

The existence of a local solution to the Sp(2) master equation for gauge field theory is proven in the framework of perturbation theory and under standard assumptions on regularity of the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided that they are proper. It is also shown that the effective action can be chosen to be Sp(2) and Lorentz invariant (under the additional assumption that the gauge transformation generators are Lorentz tensors).Comment: LaTeX, 13 pages, minor misprints correcte

Degenerate Odd Poisson Bracket on Grassmann Variables

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $\Delta$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.Comment: 5 pages, LATEX. Corrections of misprints. The relation (23) is adde

Explicit construction of the classical BRST charge for nonlinear algebras

We give an explicit formula for the Becchi-Rouet-Stora-Tyutin (BRST) charge associated with Poisson superalgebras. To this end, we split the master equation for the BRST charge into a pair of equations such that one of them is equivalent to the original one. We find the general solution to this equation. The solution possesses a graphical representation in terms of diagrams.Comment: 9 pages; v2,v3 minor corrections, references added for v

More on the Subtraction Algorithm

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta\lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations, by generalizing a well- known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space ${\cal M}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle ${\cal E}\rightarrow {\cal M}_{gf}$ with a connection $\omega_1$ is defined, such that the canonical transformations are gauge transformations for $\omega_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on ${\cal M}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\cal M}_{ph}$ of the physical parameters $\lambda$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\cal M}_{ph}$, orthogonal to ${\cal M}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on ${\cal E}$. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.Comment: LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/E

A Modified Scheme of Triplectic Quantization

A modified version of triplectic quantization, first introduce by Batalin and Martnelius, is proposed which makes use of two independent master equations, one for the action and one for the gauge functional such that the initial classical action also obeys that master equation.Comment: 8 page

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

Hamiltonian BRST-anti-BRST Theory

The hamiltonian BRST-anti-BRST theory is developed in the general case of arbitrary reducible first class systems. This is done by extending the methods of homological perturbation theory, originally based on the use of a single resolution, to the case of a biresolution. The BRST and the anti-BRST generators are shown to exist. The respective links with the ordinary BRST formulation and with the $sp(2)$-covariant formalism are also established.Comment: 34 pages, Latex fil

The unphysical nature of the SL(2,R) symmetry and its associated condensates in Yang-Mills theories

BRST cohomology methods are used to explain the origin of the SL(2,R) symmetry in Yang-Mills theories. Clear evidence is provided for the unphysical nature of this symmetry. This is obtained from the analysis of a local functional of mass dimension two and constitutes a no-go statement for giving a physical meaning to condensates associated with the symmetry breaking of SL(2,R).Comment: 5 pages (revtex4), final version to appear in Phys. Rev.

Cohomological aspects of Abelian gauge theory

We discuss some aspects of cohomological properties of a two-dimensional free Abelian gauge theory in the framework of BRST formalism. We derive the conserved and nilpotent BRST- and co-BRST charges and express the Hodge decomposition theorem in terms of these charges and a conserved bosonic charge corresponding to the Laplacian operator. It is because of the topological nature of free U(1) gauge theory that the Laplacian operator goes to zero when equations of motion are exploited. We derive two sets of topological invariants which are related to each-other by a certain kind of duality transformation and express the Lagrangian density of this theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of Witten- and Schwarz type of topological field theories.Comment: 12 pages, LaTeX, no figures, Title and text have been slightly changed, Journal reference is given and a reference has been adde

Topological 2-form Gravity in Four Dimensions

A kind of topological field theory is proposed as a candidate to describe the global structure of the 2-form Einstein gravity with or without a cosmological constant. Indeed in the former case, we show that a quantum state in the candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried out for this topological version of the 2-form Einstein gravity.Comment: 15 page