26 research outputs found

    Quantizing non-Lagrangian gauge theories: an augmentation method

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    We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in dd dimensions into an equivalent Lagrangian topological field theory in d+1d+1 dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest.Comment: 46 pages, minor correction

    Massive Spinning Particle in Any Dimension I. Integer Spins

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    The Kirillov-Souriau-Kostant construction is applied to derive the classical and quantum mechanics for the massive spinning particle in arbitrary dimension.Comment: 13 pages, LaTe

    BRST analysis of general mechanical systems

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    We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute certain cohomology groups having clear physical meaning. These include the groups of global symmetries, conservation laws and Lagrange structures. It is shown that the space of integrable Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization of general not necessarily variational dynamics by means of Lagrange structures and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde

    All Stable Characteristic Classes of Homological Vector Fields

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    An odd vector field QQ on a supermanifold MM is called homological, if Q2=0Q^2=0. The operator of Lie derivative LQL_Q makes the algebra of smooth tensor fields on MM into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator LQL_Q and are represented by QQ-invariant tensors made up of the homological vector field and a symmetric connection on MM by means of tensor operations.Comment: 17 pages, references and comments adde

    Schwinger-Dyson equation for non-Lagrangian field theory

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    A method is proposed of constructing quantum correlators for a general gauge system whose classical equations of motion do not necessarily follow from the least action principle. The idea of the method is in assigning a certain BRST operator Ω^\hat\Omega to any classical equations of motion, Lagrangian or not. The generating functional of Green's functions is defined by the equation Ω^Z(J)=0\hat\Omega Z (J) = 0 that is reduced to the standard Schwinger-Dyson equation whenever the classical field equations are Lagrangian. The corresponding probability amplitude Ψ\Psi of a field ϕ\phi is defined by the same equation Ω^Ψ(ϕ)=0\hat\Omega \Psi (\phi) = 0 although in another representation. When the classical dynamics are Lagrangian, the solution for Ψ(ϕ)\Psi (\phi) is reduced to the Feynman amplitude eiSe^{\frac{i}{\hbar}S}, while in the non-Lagrangian case this amplitude can be a more general distribution.Comment: 33 page

    Lagrange structure and quantization

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    A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in dd dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page

    Higher spins dynamics in the closed string theory

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    The general σ\sigma-model-type string action including both massless and massive higher spins background fields is suggested. Field equations for background fields are followed from the requirement of quantum Weyl invariance. It is shown that renormalization of the theory can be produced level by level. The detailed consideration of background fields structure and corresponding fields equations is given for the first massive level of the closed bosonic string.Comment: 11 pages, report TSU/QFTD-36/9

    Poisson sigma model on the sphere

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    We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page

    BRST-anti-BRST covariant theory for the second class constrained systems. A general method and examples

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    The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for second class constraints and a pair of the respective anti-BRST charges. Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly, the the BRST-anti-BRST algebra must involve a central element, related to the nonvanishing part of the constraint commutator and having no direct analogue in a first class theory. The unitarizing Hamiltonian is fixed by the requirement of the explicit BRST-anti-BRST symmetry with a much more restricted ambiguity if compare to a first class theory or split involution second class case in the nonsymmetric formulation. The general method construction is supplemented by the explicit derivation of the extended BRST symmetry generators for several examples of the second class theories, including self--dual nonabelian model and massive Yang Mills theory.Comment: 19 pages, LaTeX, 2 examples adde

    BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

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    We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections 5, 7.1, 7.2 with examples, conclusion with all basic results unchanged, corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164), added Refs. 52, 53, 54, examples for massive fields developed by 2 way
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