Finite BRST transformation and constrained systems

We establish the connection between the generating functional for the first class theories and the generating functional for the second class theories using the finite field dependent BRST (FFBRST) transformation. We show this connection with the help of explicit calculations in two different models. The generating functional of the Proca model is obtained from the generating functional of the Stueckelberg theory for massive spin 1 vector field using FFBRST transformation. In the other example we relate the generating functionals for gauge invariant and gauge variant theories for a self-dual chiral boson.     

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.     

Higher-Derivative Gravitational Coupling Between Laser Beams

The gravitational field due to laser pulse traveling along a straight waveguide with a velocity v < c is considered in the framework of higher-derivative theory of gravitation. The deflection of a probe laser pulse propagating in the vicinity of a high-power laser pulse is discussed. It is shown from a numerical comparison that the deflection of the probe laser pulse predicted by higher-derivative theory of gravitation is much less than the prediction of general relativity if the wavelength of the laser pulse is smaller than the range of the additional force.     

NSR BRST

We extend the superconformal gauge BRST formalism directly to the D = 2 off-shell (1,0) and (1,1) superspaces that are appropriate to the NSR representation of superstrings. The BRST invariances for the spinning and heterotic first quantized string actions are derived for the first time in off-shell superspace.     

BRST Renormalization

We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.     

Models for a Finite Universe

A method of constructing 3-dimensional hyperbolic manifolds is described. Because of their high degree of symmetry, these may be suitable models for a finite universe. Because their group of symmetries is different from any in the list of manifolds given in Hodgeson and Weeks (available at ftp://ftp.northnet.org/pub/weeks/snappea/closedcensus), it is claimed that these are new.     

Duality theorems in BRST cohomology

In classical mechanics, there is no duality theorem relating the BRST cohomologies at positive and negative ghost numbers since these generically fail to be isomorphic. It is shown in this paper, however, that a duality theorem for the BRST operator cohomology can be established in quantum mechanics. Furthermore, when the hermicity properties of the quantum BRST formalism—which are in general just formal—turn out to be actually well defined, this duality theorem also holds for the state cohomology, as a consequence of the non degenerate pairing between subspaces at positive and negative ghost numbers defined by the BRST scalar product. In the case of gauge systems quantized in the Schrödinger representation with compact gauge orbits, the duality theorem contains ordinary Poincaré duality for a compact manifold. In the Fock representation, the duality theorem sheds a new light on existing decoupling theorems. The comparison with the classical situation is also briefly discussed.     

BRST cohomology in superstring theories

Following the work of Freeman and Olive, it is shown that the operators counting the number of non-transverse modes of the superstrings in the Neveu-Schwarz-Ramond formalism are expressed as the anticommutators of the BRST charges Q with other operators. Also the cohomology of Q and the transverse state projection operators are discussed in terms of Q.     

Iterated BRST Cohomology

The iterated BRST cohomology is studied by computing cohomology of the variational complex on the infinite order jet space of a smooth fibre bundle. This computation also provides a solution of the global inverse problem of the calculus of variations in Lagrangian field theory.     

Finite Time Corrections in KPZ Growth Models

We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of fluctuations has been previously obtained. In this paper we consider the convergence to the limiting distributions and determine the (non-universal) first order corrections, which turn out to be a non-random shift of order t ^−1/3 (of order 1 in microscopic units). Subtracting this deterministic correction, the convergence is then of order t ^−2/3. We also determine the strength of asymmetry in the exclusion process for which the shift is zero. Finally, we discuss to what extend the discreteness of the model has an effect on the fitting functions.     

BRST cohomology in classical mechanics

The classical (non-quantum) cohomology of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry in phase space is defined and worked out. No group action for the gauge transformations is assumed. The results cover, therefore, the general case of an open algebra and are valid off-shell. Each cohomology class contains all BRST invariant functions with fixed ghost number (an integer) which differ from each other by a BRST variation. If the ghost number is negative there is only the trivial class whose elements are equivalent to zero. If the ghost number is positive or zero there is a bijective correspondence between the BRST classes and those of the exterior derivative along the gauge orbits. These gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish. The BRST invariant functions of ghost numberp are then related to closedp-forms along the orbits. The addition of a BRST variation corresponds to the addition of an exact form. Some comments about the quantum case are included. The physical meaning of the classes with ghost number greater than zero is not discussed.Chercheur qualifié du Fonds National de la Recherche Scientifique (Belgium)     

BRST quantization in the Siegel gauge

From a formal generalization to N copies of the free open string field theory BRST-quantized in the Siegel gauge we reproduce the BRST quantization of the free closed bosonic string field theory and obtain the one of massless higher spin field theories.     

BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

Hamiltonian BRST interactions in Abelian theories

Consistent couplings between an Abelian gauge field and three types of matter fields are investigated by means of the Hamiltonian BRST deformation theory based on cohomological techniques. In this manner, scalar electrodynamics, the Stuckelberg theory for Abelian zero- and one-forms, respectively, spinor electrodynamics, are inferred. Received: 6 December 2000 / Published online: 23 February 2001     

BRST invariant N-reggeon vertex

An N-reggeon vertex is constructed with the inclusion of the contribution of the ghost coordinates. It is shown that it is projective and BRST invariant.     

BRST symmetry of field redefinitions

Field redefinitions are considered as a special case of BRST gauge fixings of more general field-enlarging transformations. At the two-loop level an extra local term in the action, the Gervais-Jevicki potential, is generated by point canonical transformations in the bosonic part of the theory. We give an example of how this additional term can be cancelled by the inclusion of the ghost fields. This is achieved through an anomalous Jacobian factor from the ghost measure.     

Finite Local Models for the GHZ Experiment

Some years ago Szabó and Fine proposed a local hidden variable theory for the GHZ experiment based on the assumption that “the detection efficiency is not (only) the effect of random errors in the detector equipment, but it is a more fundamental phenomenon, the manifestation of a predetermined hidden property of the particles”. Szabó and Fine, however, did not provide a general approach to quantum phenomena which avoids nonlocality. Such an approach, based on the same assumption, was instead recently supplied by some of us and called extended semantic realism (ESR) model. We show here that one can extract from the ESR model several local finite models referring to the specific physical situation considered in the GHZ experiment, and that these models can be converted into the toy models for the GHZ experiment worked out by Szabó and Fine.     

BRST quantization of the superparticle

We show that the quantization of the superparticle action is possible. This is done by shifts in the BRST operator and the resulting action has an infinite number of ghosts. The total BRST operator is given by an infinite sum and is shown to be nilpotent. We also obtain a BRST invariant kinetic operator that contains the dynamical, auxiliary and gauge pieces in it.     

BRST Extension of Geometric Quantization

Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also BRST operators for many systems require regularization to be well-defined. In our more restricted context, we show that our treatment does not suffer from any of these difficulties.