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Robert Marnelius

Publications and source records attributed to Robert Marnelius.

36 records · Page 2Linked to original sources
arXiv1999

A general BRST approach to string theories with zeta function regularizations

We propose a new general BRST approach to string and string-like theories which have a wider range of applicability than e g the conventional conformal field theory method. The method involves a simple general regularization of all basic commutators which makes all divergent sums to be expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particular useful in order to investigate possible state space representations to a given model. The method is applied to three string models: The ordinary bosonic string, the tensionless string and the conformal tensionless string. We also investigate different state spaces for these models. The tensionless string models are treated in details. Although we mostly rederive known results they appear in a new fashion which deepens our understanding of these models. Furthermore, we believe that our treatment is more rigorous than most of the previous ones. In the case of the conformal tensionless string we find a new solution for d=4.

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arXiv1999

Quantum antibrackets

A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket as commutators to Poisson brackets. It is explained how this quantum antibracket is related to the classical antibracket and the Δ-operator in the BV-quantization. Higher quantum antibrackets are introduced in terms of generating operators, which automatically yield all their subsequent Jacobi identities as well as the consistent Leibniz' rules.

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arXiv1998

Dualities between Poisson brackets and antibrackets

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer-Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.

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arXiv1998

Open groups of constraints - Integrating arbitrary involutions

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

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arXiv1997

Antisymplectic Gauge Theories

A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed formalism for antisymplectic second class constraints through a generalized conversion to corresponding first class constraints. Thereby the basic concept of gauge symmetry is extended to apply to quite a new class of gauge theories potentially possible to exist.

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arXiv1997

Generalized BRST Quantization and Massive Vector Fields

A previously proposed generalized BRST quantization on inner product spaces for second class constraints is further developed through applications. This BRST method involves a conserved generalized BRST charge Q which is not nilpotent but which satisfies Q=δ+δ^{\dagger}, δ^2=0, and by means of which physical states are obtained from the projection δ|ph>=δ^{\dagger}|ph>=0. A simple model is analyzed in detail from which some basic properties and necessary ingredients are extracted. The method is then applied to a massive vector field. An effective theory is derived which is close to the one of the Stueckelberg model. However, since the scalar field here is introduced in order to have inner product solutions, a massive Yang-Mills theory with polynomial interaction terms might be possible to construct.

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arXiv1996

Time evolution in general gauge theories defined on inner product spaces

As previously shown BRST singlets |s> in a BRST quantization of general gauge theories on inner product spaces may be represented in the form |s>=e^{[Q, ψ]} |ϕ> where |ϕ> is either a trivially BRST invariant state which only depends on the matter variables, or a solution of a Dirac quantization. ψis a corresponding fermionic gauge fixing operator. In this paper it is shown that the time evolution is determined by the singlet states of the corresponding reparametrization invariant theory. The general case when the constraints and Hamiltonians may have explicit time dependence is treated.

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arXiv1996

General Triplectic Quantization

The general structure of the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism, the so called triplectic quantization, as presented in our previous paper with A.M.Semikhatov is further generalized and clarified. We present new unified expressions for the generating operators which are more invariant and which yield a natural realization of the operator V^a and provide for a geometrical explanation for its presence. This V^a operator provides then for an invariant definition of a degenerate Poisson bracket on the triplectic manifold being nondegenerate on a naturally defined submanifold. We also define inverses to nondegenerate antitriplectic metrics and give a natural generalization of the conventional calculus of exterior differential forms which e g explains the properties of these inverses. Finally we define and give a consistent treatment of second class hyperconstraints.

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arXiv1995

Gauge fixing and coBRST

It has previously been shown that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^[Q, ψ] |ϕ> where |ϕ> is either a trivially BRST invariant state which only depends on the matter variables, |ϕ>_1, or a solution of a Dirac quantization, |ϕ>_2. ψis a corresponding fermionic gauge fixing operator, ψ_1 or ψ_2. We show here for abelian and nonabelian models that one may also choose a linear combination of ψ_1 and ψ_2 for both choices of |ϕ> except for a discrete set of relations between the coefficients. A general form of the coBRST charge operator is also determined and shown to be equal to such a ψfor an allowed linear combination of ψ_1 and ψ_2. This means that the coBRST charge is always a good gauge fixing fermion.

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arXiv1995

Completely anticanonical form of Sp(2)-symmetric Lagrangian quantization

The Sp(2)-symmetric Lagrangian quantization scheme is represented in a completely anticanonical form. Antifields are assigned to all field variables including former "parametric" ones π^{Aa}. The antibrackets (F, G)^a as well as the operators \triangle^a and V^a are extended to include the new anticanonical pairs π^{Aa}, \barϕ_A. A new version of the gauge fixing mechanism in the Lagrangian effective action is proposed. The corresponding functional integral is shown to be gauge independent.

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arXiv1995

Solving general gauge theories on inner product spaces

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^{[Q, ψ]} |ph>_0 where Q is the nilpotent BRST operator, ψa hermitian fermionic gauge fixing operator, and |ph>_0 BRST invariant states determined by a hermitian set of BRST doublets in involution. |ph>_0 does not belong to an inner product space although |ph> does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for |ph>_0 and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that |ph>_0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set |ph>_0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.

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arXiv1995

BRST quantization of gauge theories like SL(2,R) on inner product spaces

Some general formulas are derived for the solutions of a BRST quantization on inner product spaces of finite dimensional bosonic gauge theories invariant under arbitrary Lie groups. A detailed analysis is then performed of SL(2,R) invariant models and some possible geometries of the Lagrange multipliers are derived together with explicit results for a class of SL(2,R) models. Gauge models invariant under a nonunimodular gauge group are also studied in some detail.

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arXiv1993

A note on path integrals and time evolutions in BRST quantization

Recent formal solutions of BRST quantization on inner product spaces within the operator method are shown to lead to an unexpected interpretation of the conventional path integral formulation. The relation between the Hamiltonians in the two formulations is nontrivial. For the operator method the correspondence requires certain quantum rules which make the formal solutions exact, and for the path integral the correspondence yields a precise connection between boundary conditions and the choice of gauge fixing.

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arXiv1993

Proper BRST quantization of relativistic particles

Recently derived general formal solutions of a BRST quantization on inner product spaces of irreducible Lie group gauge theories are applied to trivial models and relativistic particle models for particles with spin 0, 1/2 and 1. In the process general quantization rules are discovered which make the formal solutions exact. The treatment also give evidence that the formal solutions are directly generalizable to theories with graded gauge symmetries. For relativistic particles reasonable results are obtained although there exists no completely Lorentz covariant quantization of the coordinate and momenta on inner product spaces. There are two inequivalent procedures depending on whether or not the time coordinate is quantized with positive or indefinite metric states. The latter is connected to propagators.

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arXiv1993

Gauge fixing and abelianization in simple BRST quantization

In a previous paper \cite{Simple} it was shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as $Q=\del+\del^†,\;\;\;\del^2=\del^{†2}=0,\;\;\;[\del, \del^†]_+=0$ provided dynamical Lagrange multipliers are used but without introducing other matter variables in $\del$ than the gauge generators in $Q$. In this paper further decompositions are derived but now by means of gauge fixing operators. As in \cite{Simple} it is shown that $\del=c^{†a}ϕ_a$ where $c^a$ are new ghosts and $ϕ_a$ are nonhermitian variables satisfying the gauge algebra. However, in distinction to \cite{Simple} also solutions of the form $\del=c^{†a}A_a$ where $A_a$ satisfy an abelian algebra is derived (abelianization). By means of a bigrading the BRST condition reduces to $\del|ph\hb=\del^†|ph\hb=0$ on inner product spaces whose general solutions are expressed in terms of the solutions to a proper Dirac quantization. Thus, the procedure provides for inner products for the solutions of a Dirac quantization.

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arXiv1992

Simple BRST quantization of general gauge models

It is shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as $$Q=\del+\del^†, \del^2=\del^{†2}=0, [\del, \del^†]_+=0$$ provided dynamical Lagrange multipliers are used but without introducing other matter variables in $\del$ than the gauge generators in $Q$. Furthermore, $\del$ is shown to have the form $\del=c^{†a}ϕ_a$ (or $ϕ'_ac^{†a}$) where $c^a$ are anticommuting expressions in the ghosts and Lagrange multipliers, and where the non-hermitian operators $ϕ_a$ satisfy the same Lie algebra as the original gauge generators. By means of a bigrading the BRST condition reduces to $\del|ph\hb=\del^†|ph\hb=0$ which is naturally solved by $c^a|ph\hb=ϕ_a|ph\hb=0$ (or $c^{†a}|ph\hb={ϕ'_a}^†|ph\hb=0$). The general solutions are shown to have a very simple form.

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