Computing the BRST Operator Used in Quantization of Gauge Theories

It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of {\tt REDUCE} are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.Comment: 13 pages, plain tex with vanilla.sty included at the end of the pape

A modification of the 10d superparticle action inspired by the Gupta-Bleuler quantization scheme method

We reconsider the issue of the existence of a complex structure in the Gupta-Bleuler quantization scheme. We prove an existence theorem for the complex structure associated with the $d=10$ Casalbuoni-Brink-Schwarz superparticle, based on an explicitly constructed Lagrangian that allows a holomorphic-antiholomorphic splitting of the fermionic constraints consistent with the vanishing of all first class constraints on the physical states.Comment: 7 pages, LaTeX, to appear in Phys. Lett.

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

Free Relativistic Anyons with Canonical Spin Algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra $\left\{ S_\mu , S_\nu \right\}\,=\,\epsilon_{\mu \nu \gamma}S^\gamma$. It is shown that it is a general consequence of these features that the Poincar\`e invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.Comment: Complete version with reference

Odd Scalar Curvature in Anti-Poisson Geometry

Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure \rho if a zero-order term \nu_{\rho} is added to the \Delta operator. The effects of this odd scalar term \nu_{\rho} become relevant at two-loop order. We prove that \nu_{\rho} is essentially the odd scalar curvature of an arbitrary torsion-free connection that is compatible with both the anti-Poisson structure E and the density \rho. This extends a previous result for non-degenerate antisymplectic manifolds to degenerate anti-Poisson manifolds that admit a compatible two-form.Comment: 9 pages, LaTeX. v2: Minor changes. v3: Published versio

The effective action and quantum gauge transformations

The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can be used for construction simple gauge generators. For example, for the Yang-Mills theory the classically invariant effective action is obtained, reproducing DeWitt's result. For rank one theories a natural generalization is proposed.Comment: Revtex, 11 pages; added reference

Symmetries and dynamics in constrained systems

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total Hamiltonian systems. In particular, in analogue to total Hamiltonians, we introduce the notion of total Noether charges. Grassmannian degrees of freedom are also addressed in details.Comment: 1+97 pages, No figure, Expanded version of a lecture note by J.-H. Park at Sogang University, Seoul during 2007-2008. Accepted for publication in the European Physical Journal C as a review article; Reference adde

Treatment outcome in infant acute lymphoblastic leukemia

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Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

First order parent formulation for generic gauge field theories

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction