Remarks on the general solution for the flat Friedman universe with exponential scalar-field potential and dust

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails and we discuss the reasons of this puzzling phenomenon.Comment: 11 page

Perfect and Imperfect Gauge Fixing

Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system, enables us to use either a perfect gauge, in which all gauged degrees of freedom are determined; or an imperfect gauge, in which some first class constraints remain as subsidiary conditions to be imposed on the solutions of the equations of motion. We also show that the number of constants of motion depends on the level in a constraint chain in which the gauge fixing condition is imposed. The relativistic point particle, electromagnetism and the Polyakov string are discussed as examples and perfect or imperfect gauges are distinguished.Comment: 19 pages, no figur

Substituting fields within the action: consistency issues and some applications

In field theory, as well as in mechanics, the substitution of some fields in terms of other fields at the level of the action raises an issue of consistency with respect to the equations of motion. We discuss this issue and give an expression which neatly displays the difference between doing the substitution at the level of the Lagrangian or at the level of the equations of motion. Both operations do not commute in general. A very relevant exception is the case of auxiliary variables, which are discussed in detail together with some of their relevant applications. We discuss the conditions for the preservation of symmetries - Noether as well as non-Noether - under the reduction of degrees of freedom provided by the mechanism of substitution. We also examine how the gauge fixing procedures fit in our framework and give simple examples on the issue of consistency in this case.Comment: 17 page

Tensor Coordinates in Noncommutative Mechanics

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly used, and the object of noncommutativity ${\mathbf \theta}^{ij}$ plays a fundamental rule as an independent quantity. The presented classical theory, as its quantum counterpart, is naturally invariant under the rotation group $SO(D)$.Comment: 12 pages, Late

Revisiting observables in generally covariant theories in the light of gauge fixing methods

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates accomplished with the aid of spacetime scalar fields. With our approach we make full contact with, and give a new perspective to, the "evolving constants of motion" program. We are able to directly derive generic properties of observables, especially their dynamics and their Poisson algebra in terms of Dirac brackets, extending earlier results in the literature. We also give a new interpretation of the observables as limits of canonical maps

Gauge invariances vis-{\'a}-vis Diffeomorphisms in second order metric gravity: A new Hamiltonian approach

A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.Comment: 6 Pages, revTex, paper modified substantiall

Gravitational observables, intrinsic coordinates, and canonical maps

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism transformations has remained obscure. In a symmetry-inspired approach we construct invariants out of canonically induced active gauge transformations. These invariants may be intepreted as the full set of dynamical variables evaluated in the intrinsic coordinate system. The functional invariants can explicitly be written as a Taylor expansion in the coordinates of any observer, and the coefficients have a physical and geometrical interpretation. Surprisingly, all invariants can be obtained as limits of a family of canonical transformations. This permits a short (again geometric) proof that all invariants, including the lapse and shift, satisfy Poisson brackets that are equal to the invariants of their corresponding Dirac brackets.Comment: 4 pages, to appear in Modern Physics Letters

BRST Hamiltonian for Bulk-Quantized Gauge Theory

By treating the bulk-quantized Yang-Mills theory as a constrained system we obtain a consistent gauge-fixed BRST hamiltonian in the minimal sector. This provides an independent derivation of the 5-d lagrangian bulk action. The ground state is independent of the (anti)ghosts and is interpreted as the solution of the Fokker-Planck equation, thus establishing a direct connection to the Fokker-Planck hamiltonian. The vacuum state correlators are shown to be in agreement with correlators in lagrangian 5-d formulation. It is verified that the complete propagators remain parabolic in one-loop dimensional regularization.Comment: 23 pages, AMS-LaTeX, 1 feynmf diagram, added 2 refs email addres

On the Effectiveness of Neural Text Generation based Data Augmentation for Recognition of Morphologically Rich Speech

Advanced neural network models have penetrated Automatic Speech Recognition (ASR) in recent years, however, in language modeling many systems still rely on traditional Back-off N-gram Language Models (BNLM) partly or entirely. The reason for this are the high cost and complexity of training and using neural language models, mostly possible by adding a second decoding pass (rescoring). In our recent work we have significantly improved the online performance of a conversational speech transcription system by transferring knowledge from a Recurrent Neural Network Language Model (RNNLM) to the single pass BNLM with text generation based data augmentation. In the present paper we analyze the amount of transferable knowledge and demonstrate that the neural augmented LM (RNN-BNLM) can help to capture almost 50% of the knowledge of the RNNLM yet by dropping the second decoding pass and making the system real-time capable. We also systematically compare word and subword LMs and show that subword-based neural text augmentation can be especially beneficial in under-resourced conditions. In addition, we show that using the RNN-BNLM in the first pass followed by a neural second pass, offline ASR results can be even significantly improved.Comment: 8 pages, 2 figures, accepted for publication at TSD 202

Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field and non-linear sigma model.Comment: 17 pages, to be published in Phys. Rev.