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D. S. Kaparulin

Publications and source records attributed to D. S. Kaparulin.

30 records · Page 2Linked to original sources
arXiv2017

Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons

Most general third-order $3d$ linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the zero-zero components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations.

hep-th↗
arXiv2017

Correlations between planetary transit timing variations, transit duration variations and brightness fluctuations due to exomoons

Modern theoretical estimates show that with the help of real equipment we are able to detect large satellites of exoplanets (about the size of the Ganymede), although, numerical attempts of direct exomoon detection were unsuccessful. Lots of methods for finding the satellites of exoplanets for various reasons have not yielded results. Some of the proposed methods are oriented on a more accurate telescopes than those exist today. In this work, we propose a method based on relationship between the transit timing variation (TTV) and the brightness fluctuations (BF) before and after the planetary transit. With the help of a numerical simulation of the Earth-Moon system transits, we have constructed data on the BF and the TTV for any configuration of an individual transit. The experimental charts obtained indicate an easily detectable near linear dependence. Even with an artificial increase in orbital speed of the Moon and high-level errors in measurements the patterns suggest an accurate correlation. A significant advantage of the method is its convenience for multiple moons systems due to an additive properties of the TTV and the BF. Its also important that mean motion resonance (MMR) in system have no affect on ability of satellites detection. At the end we tried to retrieve parameters of the Moon (without additional satellites) on the basis of the simulated photometric curves. The results perform errors at the level of $\approx 0.45$ for the mass and $\approx 0.24$ for the radius with TTV measurements accuracy =60s and Kepler-like noise for photometry.

astro-ph.IM↗
arXiv2016

Stable interactions via proper deformations

A new method is proposed for switching on interactions that are compatible with global symmetries and conservation laws of the original free theory. The method is applied to the control of stability in Lagrangian and non-Lagrangian theories with higher derivatives. By way of illustration, a wide class of stable interactions is constructed for the Pais-Uhlenbeck oscillator.

hep-th↗
arXiv2015

Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability

We consider the class of higher derivative $3d$ vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For $n$-th order theory of this type, we provide a general receipt for constructing $n$-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

hep-th↗
arXiv2015

Energy and stability of Pais-Uhlenbeck oscillator

We study stability of higher-derivative dynamics from the viewpoint of more general correspondence between symmetries and conservation laws established by the Lagrange anchor. We show that classical and quantum stability may be provided if a higher-derivative model admits a bounded from below integral of motion and the Lagrange anchor that relates this integral to the time translation.

hep-th↗
arXiv2014

Classical and quantum stability of higher-derivative dynamics

We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that keep the system stable.

hep-th↗
arXiv2013

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.

math-ph↗
arXiv2013

Lagrange Anchor for Bargmann-Wigner equations

A Poincare invariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin s > 1/2 in four-dimensional Minkowski space. By making use of this Lagrange anchor, we assign a symmetry to each conservation law.

math-ph↗
arXiv2013

Consistent interactions and involution

Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is explicitly covariant. No auxiliary fields are introduced. The equations may have (or have no) gauge symmetry and/or second class constraints in Hamiltonian formalism, providing the theory admits a Hamiltonian description. In every case the method identifies all the consistent interactions.

hep-th↗
arXiv2011

Local BRST cohomology in (non-)Lagrangian field theory

Some general theorems are established on the local BRST cohomology for not necessarily Lagrangian gauge theories. Particular attention is given to the BRST groups with direct physical interpretation. Among other things, the groups of rigid symmetries and conservation laws are shown to be still connected, though less tightly than in the Lagrangian theory. The connection is provided by the elements of another local BRST cohomology group whose elements are identified with Lagrange structures. This extends the cohomological formulation of the Noether theorem beyond the scope of Lagrangian dynamics. We show that each integrable Lagrange structure gives rise to a Lie bracket in the space of conservation laws, which generalizes the Dickey bracket of conserved currents known in Lagrangian field theory. We study the issues of existence and uniqueness of the local BRST complex associated with a given set of field equations endowed with a compatible Lagrange structure. Contrary to the usual BV formalism, such a complex does not always exist for non-Lagrangian dynamics, and when exists it is by no means unique. The ambiguity and obstructions are controlled by certain cohomology classes, which are all explicitly identified.

hep-th↗
arXiv2010

A remark on the Lagrange structure of the unfolded field theory

Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the concept of Lagrange anchor is applied to perform a consistent path-integral quantization of unfolded dynamics. It is shown that the unfolded representation for the canonical Lagrange anchor of the d'Alembert equation inevitably involves an infinite number of space-time derivatives.

hep-th↗