100 research outputs found
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 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 . 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
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
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