Abelian 3-form gauge theory: superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow Region, Russi

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ

Free field representation of Toda field theories

We study the following problem: can a classical $sl_n$ Toda field theory be represented by means of free bosonic oscillators through a Drinfeld--Sokolov construction? We answer affirmatively in the case of a cylindrical space--time and for real hyperbolic solutions of the Toda field equations. We establish in fact a one--to--one correspondence between such solutions and the space of free left and right bosonic oscillators with coincident zero modes. We discuss the same problem for real singular solutions with non hyperbolic monodromy.Comment: 29 pages, Latex, SISSA-ISAS 210/92/E

Nilpotent (anti-)BRST symmetry transformations for dynamical non-Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the dynamical non-Abelian 2-form gauge theory within the framework of geometrical superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian densities that respect the above nilpotent symmetry transformations. We discuss, furthermore, this (anti-) BRST invariance in the language of the superfield formalism. One of the novel features of our investigation is the observation that, in addition to the horizontality condition, we have to invoke some other physically relevant restrictions to deduce the exact (anti-) BRST symmetry transformations for all the fields of the topologically massive non-Abelian gauge theory.Comment: LaTeX file, 8 pages, typos fixed in some equations, journal-versio

BRST analysis of topologically massive gauge theory: novel observations

A dynamical non-Abelian 2-form gauge theory (with B \wedge F term) is endowed with the "scalar" and "vector" gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the four (3 + 1)-dimensional (4D) topologically massive non-Abelian 2-form gauge theory. We demonstrate the existence of some novel features that have, hitherto, not been observed in the context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form and 3-form gauge theories. We comment on the differences between the novel features that emerge in the BRST analysis of the "scalar" and "vector" gauge symmetries of the theory.Comment: LaTeX file, 14 pages, an appendix added, references expanded, version to appear in EPJ

Opening the Pandora's box of quantum spinor fields

Lounesto's classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.Comment: 18 page

Notoph Gauge Theory: Superfield Formalism

We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticommutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.Comment: LaTeX file, 12 pages, Talk delivered at SQS'09 (BLTP, JINR, Dubna

BRST, anti-BRST and their geometry

We continue the comparison between the field theoretical and geometrical approaches to the gauge field theories of various types, by deriving their Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and comparing them with the geometrical properties of the bundles and gerbes. In particular, we provide the geometrical interpretation of the so--called Curci-Ferrari conditions that are invoked for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations in the context of non-Abelian 1-form gauge theories as well as Abelian gauge theory that incorporates a 2-form gauge field. We also carry out the explicit construction of the 3-form gauge fields and compare it with the geometry of 2--gerbes.Comment: A comment added. To appear in Jour. Phys. A: Mathemaical and Theoretica

Dirac, Majorana, Weyl in 4d

This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4d. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularizations. Among various well known results we stress in particular the regularization independence in perturbative approaches, while not all the regularizations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.Comment: 38 pages, 3 figures, section 5, Appendix A and Appendix C new, several typos correcte

W-infinity structure of the sl(N)sl(N) conformal affine Toda theories

We reexamine the $W_{\infty}$ symmetry of the $sl(N)$ Conformal Affine Toda theories. It is shown that it is possible to reduce (nonuniquely) the zero curvature equation to a Lax equation for a first order pseudodifferential oprator, whose coefficients are the generators of the $W_{\infty}$ algebra. This clarifies the known relation between the Conformal Affine Toda theories and the KP hierarchy. A possible correspondence between the matrix models and the Conformal Affine Toda models is discussed.Comment: 13 page