466 research outputs found

### Triplectic Gauge Fixing for N=1 Super Yang-Mills Theory

The Sp(2)-gauge fixing of N = 1 super-Yang-Mills theory is considered here.
We thereby apply the triplectic scheme, where two classes of gauge-fixing
bosons are introduced. The first one depends only on the gauge field, whereas
the second boson depends on this gauge field and also on a pair of Majorana
fermions. In this sense, we build up the BRST extended (BRST plus antiBRST)
algebras for the model, for which the nilpotency relations,
s^2_1=s^2_2=s_1s_2+s_2s_1=0, hold.Comment: 10 pages, no figures, latex forma

### 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

### Gauge theory of second class constraints without extra variables

We show that any theory with second class constraints may be cast into a
gauge theory if one makes use of solutions of the constraints expressed in
terms of the coordinates of the original phase space. We perform a Lagrangian
path integral quantization of the resulting gauge theory and show that the
natural measure follows from a superfield formulation.Comment: 12 pages, Latexfil

### Triplectic Quantization of W2 gravity

The role of one loop order corrections in the triplectic quantization is
discussed in the case of W2 theory. This model illustrates the presence of
anomalies and Wess Zumino terms in this quantization scheme where extended BRST
invariance is represented in a completely anticanonical form.Comment: 10 pages, no figure

### Geometry of Batalin-Vilkovisky quantization

The present paper is devoted to the study of geometry of Batalin-Vilkovisky
quantization procedure. The main mathematical objects under consideration are
P-manifolds and SP-manifolds (supermanifolds provided with an odd symplectic
structure and, in the case of SP-manifolds, with a volume element). The
Batalin-Vilkovisky procedure leads to consideration of integrals of the
superharmonic functions over Lagrangian submanifolds. The choice of Lagrangian
submanifold can be interpreted as a choice of gauge condition; Batalin and
Vilkovisky proved that in some sense their procedure is gauge independent. We
prove much more general theorem of the same kind. This theorem leads to a
conjecture that one can modify the quantization procedure in such a way as to
avoid the use of the notion of Lagrangian submanifold. In the next paper we
will show that this is really so at least in the semiclassical approximation.
Namely the physical quantities can be expressed as integrals over some set of
critical points of solution S to the master equation with the integrand
expressed in terms of Reidemeister torsion. This leads to a simplification of
quantization procedure and to the possibility to get rigorous results also in
the infinite-dimensional case. The present paper contains also a compete
classification of P-manifolds and SP-manifolds. The classification is
interesting by itself, but in this paper it plays also a role of an important
tool in the proof of other results.Comment: 13 page

### Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class
constrained system on a symplectic manifold. The constraints determining an
arbitrary constraint surface are in general defined only locally and can be
components of a section of a non-trivial vector bundle over the phase-space
manifold. The covariance of the construction with respect to the change of the
constraint basis is provided by introducing a connection in the ``constraint
bundle'', which becomes a key ingredient of the conversion procedure for the
non-scalar constraints. Unlike in the case of scalar second-class constraints,
no Abelian conversion is possible in general. Within the BRST framework, a
systematic procedure is worked out for converting non-scalar second-class
constraints into non-Abelian first-class ones. The BRST-extended system is
quantized, yielding an explicitly covariant quantization of the original
system. An important feature of second-class systems with non-scalar
constraints is that the appropriately generalized Dirac bracket satisfies the
Jacobi identity only on the constraint surface. At the quantum level, this
results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page

### On the multilevel generalization of the field--antifield formalism

The multilevel geometrically--covariant generalization of the
field--antifield BV--formalism is suggested. The structure of quantum
generating equations and hypergauge conditions is studied in details. The
multilevel formalism is established to be physically--equivalent to the
standard BV--version.Comment: 10 pages, FIAN/TD/13--9

### On possible generalizations of field--antifield formalism

A generalized version is proposed for the field-antifield formalism. The
antibracket operation is defined in arbitrary field-antifield coordinates. The
antisymplectic definitions are given for first- and second-class constraints.
In the case of second-class constraints the Dirac's antibracket operation is
defined. The quantum master equation as well as the hypergauge fixing procedure
are formulated in a coordinate-invariant way. The general hypergauge functions
are shown to be antisymplectic first-class constraints whose Jacobian matrix
determinant is constant on the constraint surface. The BRST-type generalized
transformations are defined and the functional integral is shown to be
independent of the hypergauge variations admitted. In the case of reduced phase
space the Dirac's antibrackets are used instead of the ordinary ones

### On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to
be equivalent perturbatively to each other. It is shown in particular that the
quantum master equation being treated perturbatively possesses a local formal
solution.Comment: 14 pages, LaTeX, no figure

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