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Robert Marnelius

Publications and source records attributed to Robert Marnelius.

At least 19 recordsLinked to original sources
arXiv2009

Lagrangian higher spin field theories from the O(N) extended supersymmetric particle

The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using only the basic quantum operators which include graded external differentials, trace operators, index structure operators and their duals. The resulting equations for the gauge fields are of first (N odd) or second order (N even) and are shown to be generalized (Fang)-Fronsdal equations which are fully gauge invariant since they include compensator fields in a natural way. Local gauge invariant actions are first derived in analogy with the derivation by Francia and Sagnotti in the symmetric case. Then a minimal formulation is given within which it is easy to set up gauge invariant actions and here appropriate actions for the above equations are proposed. In a second part it is shown that there exist projection operators from the states of the field strengths (wave functions) to Weyl states (Weyl tensors) expressed only in terms of the trace operators and their duals for integer spins or in terms of the gamma trace operators and their duals for half-integer spins. These Weyl states are not just fully gauge invariant but also invariant under generalized Weyl transformations. If one lets the equations be determined by the actions defined to be the squares of these Weyl tensors then the theory is conformally invariant and the equations are of order N for the gauge fields defined as in the exact theory. In d=4 this higher order conformal theory fits into the framework for conformal higher spin theories set up by Fradkin, Tseytlin and Linetski.

hep-th↗
arXiv2008

Lagrangian conformal higher spin theory

In a previous paper conformal gravity was derived by means of a precise action principle on the hypercone in the conformal space. Here it is shown that the same technique used to construct conformal spin two theory as represented by linear conformal gravity may also be used for the construction of conformal higher spin theories. The basic ingredients in these constructions are gauge invariant field strengths (curvatures). In fact, their very existence as manifestly conformal fields requires the present conformal theory. The general form of the actions for the free theories on the hypercone are given. In spacetime these actions are shown to be expressed in terms of squares of generalized Weyl tensors. Conformal spin three and four are calculated explicitly. The theories are proposed to be equivalent to the free theories given by Fradkin and Linetsky. Since the equations are of order 2s a consistent quantization is difficult to achieve but might exist. Interactions are expected to exist and is the motivation behind this approach.

hep-th↗
arXiv2006

Conformal theories including conformal gravity as gauge theories on the hypercone

Conformal theories in a d dimensional spacetime may be expressed as manifestly conformal theories in a d+2 dimensional conformal space as first proposed by Dirac. The reduction to d dimensions goes via the d+1 dimensional hypercone in the conformal space. Here we give a rather extensive expose of such theories. We review and extend the theory of spinning conformal particles. We give a precise and geometrical formulation of manifestly conformal fields for which we give a consistent action principle. The requirement of invariance under special gauge transformations off the hypercone plays a fundamental role here. Maxwell's theory and linear conformal gravity are derived in the conformal space and are treated in detail. Finally, we propose a consistent coordinate invariant action principle in the conformal space and give an action that should correspond to conformal gravity.

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arXiv2006

Covariant quantization of infinite spin particle models, and higher order gauge theories

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in the quantization process. A consistent covariant quantization is shown to exist. Also a recently proposed supersymmetric version for half-odd integer spins is quantized. A general algorithm to derive gauge invariances of higher order Lagrangians is given and applied to the infinite spin particle model, and to a new higher order model for a spinning particle which is proposed here, as well as to a previously given higher order rigid particle model. The latter two models are also covariantly quantized.

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arXiv2005

Infinite spin particles

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to light-like accelerations. A simple higher order superversion for half-odd integer particles is also derived. Interaction with external vector fields and curved spacetimes are analyzed with negative results except for (anti)de Sitter spacetimes. We quantize the free theories covariantly and show that the resulting wave functions are fields containing arbitrary large spins. Closely related infinite spin particle models are also analyzed.

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arXiv2002

Projection operator approach to general constrained systems

We propose a new BRST-like quantization procedure which is applicable to dynamical systems containing both first and second class constraints. It requires no explicit separation into first and second class constraints and therefore no conversion of second class constraints is needed. The basic ingredient is instead an invariant projection operator which projects out the maximal subset of constraints in involution. The hope is that the method will enable a covariant quantization of models for which there is no covariant separation into first and second class constraints. An example of this type is given.

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arXiv2001

Extended observables in theories with constraints

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in the enveloping unconstrained phase space. These expressions satisfy in the unconstrained phase space a Poisson algebra of the same form as the Dirac bracket algebra of the observables on the constraint surface. The general formulas involve new differential operators that differentiate the Dirac bracket. Similar extended observables are also constructed for theories with first class constraints which, however, are gauge dependent. For such theories one may also construct gauge invariant extensions with similar properties. Whenever extended observables exist the theory is expected to allow for a covariant quantization. A mapping procedure is proposed for covariant quantization of theories with second class constraints.

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arXiv2001

Superfield algorithms for topological field theories

A superfield algorithm for master actions of a class of gauge field theories including topological ones in arbitrary dimensions is presented generalizing a previous treatment in two dimensions. General forms for master actions in superspace are given, and possible theories are determined by means of a ghost number prescription and the master equations. The resulting master actions determine the original actions together with their gauge invariances. Generalized Poisson sigma models in arbitrary dimensions are constructed by means of this algorithm, and other applications in low dimensions are given including the Chern-Simon model.

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arXiv2001

Generalized Poisson sigma models

A general master action in terms of superfields is given which generates generalized Poisson sigma models by means of a natural ghost number prescription. The simplest representation is the sigma model considered by Cattaneo and Felder. For Dirac brackets considerably more general models are generated.

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arXiv2001

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.

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arXiv2000

Quantum BRST properties of reparametrization invariant theories

Any regular quantum mechanical system may be cast into an abelian gauge theory by simply reformulating it as a reparametrization invariant theory. We present a detailed study of the BRST quantization of such reparametrization invariant theories within a precise operator version of BRST. The treatment elucidates several intricate aspects of the BRST quantization of reparametrization invariant theories like the appearance of physical time. We propose general rules for how physical wave functions and physical propagators are to be projected from the BRST singlets and propagators in the ghost extended BRST theory. These projections are performed by boundary conditions which are precisely specified by the operator BRST. We demonstrate explicitly the validity of these rules for the considered class of models. The corresponding path integrals are worked out explicitly and compared with the conventional BFV path integral formulation.

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arXiv2000

On the quantum BRST structure of classical mechanics

The BRST-antiBRST invariant path integral formulation of classical mechanics of Gozzi et al is generalized to pseudomechanics. It is shown that projections to physical propagators may be obtained by BRST-antiBRST invariant boundary conditions. The formulation is also viewed from recent group theoretical results within BRST-antiBRST invariant theories. A natural bracket expressed in terms of BRST and antiBRST charges in the extended formulation is shown to be equal to the Poisson bracket. Several remarks on the operator formulation are made.

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arXiv1999

Open group transformations within the Sp(2)-formalism

Previously we have shown that open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of the nilpotent BFV-BRST charge operator. Here we show that they may also be quantized within an Sp(2)-frame in which there are two odd anticommuting operators called Sp(2)-charges. Previous results for finite open group transformations are generalized to the Sp(2)-formalism. We show that in order to define open group transformations on the whole ghost extended space we need Sp(2)-charges in the nonminimal sector which contains dynamical Lagrange multipliers. We give an Sp(2)-version of the quantum master equation with extended Sp(2)-charges and a master charge of a more involved form, which is proposed to represent the integrability conditions of defining operators of connection operators and which therefore should encode the generalized quantum Maurer-Cartan equations for arbitrary open groups. General solutions of this master equation are given in explicit form. A further extended Sp(2)-formalism is proposed in which the group parameters are quadrupled to a supersymmetric set and from which all results may be derived.

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arXiv1999

Open group transformations

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV-BRST charge operator. Previously we have shown that generalized quantum Maurer-Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV-BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.

hep-th↗
arXiv1999

Quantum Sp(2)-antibrackets and open groups

The recently presented quantum antibrackets are generalized to quantum Sp(2)-antibrackets. For the class of commuting operators there are true quantum versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a generalized bracket structure involving higher Sp(2)-antibrackets. It is shown that these quantum antibrackets may be obtained from generating operators involving operators in arbitrary involutions. A recently presented quantum master equation for operators, which was proposed to encode generalized quantum Maurer-Cartan equations for arbitrary open groups, is generalized to the Sp(2) formalism. In these new quantum master equations the generalized Sp(2)-brackets appear naturally.

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arXiv1999

Basics of BRST quantization on inner product spaces

There is an elaborated abstract form of BRST quantization on inner product spaces within the operator formalism which leads to BRST invariant states of the form |ph>=e^{[Q,ψ]} |ϕ> where ψis a gauge fixing fermion, and where |ϕ> is a BRST invariant state determined by simple hermitian conditions. These state representations are closely related to the path integral formulation. Here we analyse the basics of this approach in detail. The freedom in the choice of ψand |ϕ> as well as their properties under gauge transformations are explicitly determined for simple abelian models. In all considered cases SL(2,R) is shown both to be a natural extended gauge symmetry and to be useful to determine |ph>. The results are also applied to nonabelian models.

hep-th↗
arXiv1999

General quantum antibrackets

The recently introduced quantum antibracket is further generalized allowing for the defining odd operator Q to be arbitrary. We give exact formulas for higher quantum antibrackets of arbitrary orders and their generalized Jacobi identities. Their applications to BV-quantization and BFV-BRST quantization are then reviewed including some new aspects.

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