113 research outputs found
Superfield Formulation of the Phase Space Path Integral
We give a superfield formulation of the path integral on an arbitrary curved
phase space, with or without first class constraints. Canonical tranformations
and BRST transformations enter in a unified manner. The superpartners of the
original phase space variables precisely conspire to produce the correct path
integral measure, as Pfaffian ghosts. When extended to the case of second-class
constraints, the correct path integral measure is again reproduced after
integrating over the superpartners. These results suggest that the superfield
formulation is of first-principle nature.Comment: 6 pages, LaTe
Unified Constrained Dynamics
The unified constrained dynamics is formulated without making use of the
Dirac splitting of constraint classes. The strengthened, completely--closed,
version of the unified constraint algebra generating equations is given. The
fundamental phase variable supercommutators are included into the unified
algebra as well. The truncated generating operator is defined to be nilpotent
in terms of which the Unitarizing Hamiltonian is constructed.Comment: Lebedev Inst. preprint, 20 p
On Generalized Gauge-Fixing in the Field-Antifield Formalism
We consider the problem of covariant gauge-fixing in the most general setting
of the field-antifield formalism, where the action W and the gauge-fixing part
X enter symmetrically and both satisfy the Quantum Master Equation. Analogous
to the gauge-generating algebra of the action W, we analyze the possibility of
having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing
algebra of the so-called first-stage in full detail and generalize to arbitrary
stages. The associated "square root" measure contributions are worked out from
first principles, with or without the presence of antisymplectic second-class
constraints. Finally, we consider an W-X alternating multi-level
generalization.Comment: 49 pages, LaTeX. v2: Minor changes + 1 more reference. v3,v4,v5:
Corrected typos. v5: Version published in Nuclear Physics B. v6,v7:
Correction to the published version added next to the Acknowledgemen
Reducible Gauge Algebra of BRST-Invariant Constraints
We show that it is possible to formulate the most general first-class gauge
algebra of the operator formalism by only using BRST-invariant constraints. In
particular, we extend a previous construction for irreducible gauge algebras to
the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd,
mutually anticommuting BRST operators that bear structural similarities with
BRST/anti-BRST theories but with shifted ghost number assignments. In both
cases we show how the extended BRST algebra can be encoded into an operator
master equation. A unitarizing Hamiltonian that respects the two BRST
symmetries is constructed with the help of a gauge-fixing Boson. Abelian
reducible theories are shown explicitly in full detail, while non-Abelian
theories are worked out for the lowest reducibility stages and ghost momentum
ranks.Comment: 42 pages, LaTeX. v2: New material added to Sec. 3.9-3.10, Sec. 6 and
App. E. v3: Version published in Nuclear Physics B. v4: Grant number adde
General solution of classical master equation for reducible gauge theories
We give the general solution to the classical master equation (S,S)=0 for
reducible gauge theories. To this aim, we construct a new coordinate system in
the extended configuration space and transform the equation by changing
variables. Then it can be solved by an iterative method.Comment: 15 pages; v3: refs. added, section 4 substantially improved, a
section added; v4: reference and example adde
Triplectic Quantization: A Geometrically Covariant Description of the Sp(2)-symmetric Lagrangian Formalism
A geometric description is given for the Sp(2) covariant version of the
field-antifield quantization of general constrained systems in the Lagrangian
formalism. We develop differential geometry on manifolds in which a basic set
of coordinates (`fields') have two superpartners (`antifields'). The
quantization on such a triplectic manifold requires introducing several
specific differential-geometric objects, whose properties we study. These
objects are then used to impose a set of generalized master-equations that
ensure gauge-independence of the path integral. The theory thus quantized is
shown to extend to a level-1 theory formulated on a manifold that includes
antifields to the Lagrange multipliers. We also observe intriguing relations
between triplectic and ordinary symplectic geometry.Comment: Revised version -- our treatment in Section 5 has been extended and
several pedagogical notes inserted in Sections 2--4; more references added
Lagrangian Becchi-Rouet-Stora-Tyutin treatment of collective coordinates
The Becchi-Rouet-Stora-Tyutin (BRST) treatment for the quantization of
collective coordinates is considered in the Lagrangian formalism. The motion of
a particle in a Riemannian manifold is studied in the case when the classical
solutions break a non-abelian global invariance of the action. Collective
coordinates are introduced, and the resulting gauge theory is quantized in the
BRST antifield formalism. The partition function is computed perturbatively to
two-loops, and it is shown that the results are independent of gauge-fixing
parameters.Comment: LaTeX file, 26 pages, PostScript figures at end of fil
Relating the generating functionals in field/antifield formulation through finite field dependent BRST transformation
We study the field/antifield formulation of pure Yang Mills theory in the
framework of finite field dependent BRST transformation. We show that the
generating functionals corresponding to different solutions of quantum master
equation are connected through the finite field dependent BRST transformations.
We establish this result with the help of several explicit examples.Comment: Revtex4, 18 pages, No figs, Accepted in Eur. Phys. J
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
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