26 research outputs found

### Quantizing non-Lagrangian gauge theories: an augmentation method

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 $d$ dimensions into an equivalent Lagrangian
topological field theory in $d+1$ 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

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

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

An odd vector field $Q$ on a supermanifold $M$ is called homological, if
$Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth
tensor fields on $M$ 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 $L_Q$ and are represented by $Q$-invariant tensors made up of the
homological vector field and a symmetric connection on $M$ by means of tensor
operations.Comment: 17 pages, references and comments adde

### Schwinger-Dyson equation for non-Lagrangian field theory

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 $\hat\Omega$ to any classical equations of motion, Lagrangian or not.
The generating functional of Green's functions is defined by the equation
$\hat\Omega Z (J) = 0$ that is reduced to the standard Schwinger-Dyson equation
whenever the classical field equations are Lagrangian. The corresponding
probability amplitude $\Psi$ of a field $\phi$ is defined by the same equation
$\hat\Omega \Psi (\phi) = 0$ although in another representation. When the
classical dynamics are Lagrangian, the solution for $\Psi (\phi)$ is reduced to
the Feynman amplitude $e^{\frac{i}{\hbar}S}$, while in the non-Lagrangian case
this amplitude can be a more general distribution.Comment: 33 page

### Lagrange structure and quantization

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 $d+1$ dimensions, being localized on the boundary, are proved to
be equivalent to the original theory in $d$ 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

The general $\sigma$-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

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

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

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