Robert Marnelius

Canonical quantization of polyakov's string in arbitrary dimensions

Last year Polyakov discovered the important role the trace anomaly plays in the relativistic string theory. This result means that one has to add counter terms to the string lagrangian nL=Lstring+CL1, n, where L1 contains a cosmological term and a term from the trace anomaly. In the conformal gauge we have nL1=LLiouville. n. We give a conventional GGRT treatment of this modified lagrangian for the bosonic string. Under the assumption that the exact quantization of Liouvilles equation does not yield any additional anomalies, we show that relativistic invariance requires the constant C to be C = 26 − D48π, in agreement with Polyakovs result. For D < 26 the string acquires longitudinal modes, and our calculations show explicitly how the longitudinal component of the string receives the degrees of freedom from the Liouville variable. Under the boundary conditions yielding the lowest value of the classical Liouville hamiltonian, the mass spectrum starts with a tachyon m2 = −1α′, independent of D. The lowest-lying longitudinal excitation is m2 = 1α′. These results are semiclassical. It is shown that an exact quantization of Liouvilles equation could remove the tachyon state when D < 26.

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.

Principles of BRST quantization

Abstract The BRST quantization as a quantization method ised. It is pointed out that all formal manipulations are only valid if all inner products in the original state space are finite. This restriction is also shown to be necessary in order to obtain the correct results for trivial models. It is argued that the investigations of BRST invariant states of the form | M 〉| G 〉, where M and G denote matter and ghost states, are sufficient to determine the physics of the BRST invariant subspace. A prescription of how to solve Q | M 〉| G 〉 = 0 is given for a general class of models. Solutions are classified into canonical and noncanonical ones. The latter cannot be obtained in a canonical quantization of the corresponding gauge model.

Generalized Poisson sigma models

Abstract 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.

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

Abstract 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 πAa. The antibrackets (F,G)a as well as the operators Δa and Va are extended to include the new anticanonical pairs πAa, Φ A . A new version of the gauge fixing mechanism i the Lagrangian effective action is proposed. The corresponding functional integral is shown to be gauge independent.

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.

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, psi]} |ph>_0 where Q is the nilpotent BRST operator, psi a 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 psi. 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.

General quantum antibrackets

The recently introduced quantum antibracket is further generalized such that the odd operator Q can be arbitrary. We give exact formulas for quantum antibrackets of arbitrary higher orders and for their generalized Jacobi identities. We review applications of the quantum antibrackets to the BV and BFV-BRST quantizations and include some new aspects.

A simple relation between covariant and noncovariant quantization of gauge theories

Abstract A general gauge theory contains a set of first class constraints G a ( x ) ≈ 0 which in the quantization procedure may be used to project out physical states G a (x)| phys > = 0 . This is contrast treatment where one only needs a single conserved global supercharge Q ( Q 2 = 0) for the same purpose: ( a ) Q |; phys > = 0 . In Yang-Mills theories Q generates BRS-transformations and (a) yield all Slavnov identies. We give a simple algebraic proof of the equivalence of the two formulations for Yang-Mills theories as well as more general covariant-type theories as formulated by Fradkin and Vilkovisky.

BRST symmetry and a general ghost decoupling theorem

Abstract A no-ghost theorem is proven in the BRST approach to quantization of a gauge theory. The proof is given in a general and model independent formulation. Two distinct classes of quantum matter states are identified and it is shown that only for one of these classes does the BRST symmetry always ensure ghost decoupling.