scholarly journals Hamiltonian analysis and positivity of a newmassive spin-2 model

2021 ◽  
Author(s):  
Alessandro Luiz Ribeiro dos Santos ◽  
Denis Dalmazi ◽  
Wayne Leonardo Silva de Paula
Keyword(s):  
Correlation Functions ◽  
Degrees Of Freedom ◽  
Spin Projection ◽  
Projection Operators ◽  
Gauge Invariant ◽  
New Model ◽  
Mixed Symmetry ◽  
Massive Spin ◽  
Rank 2 ◽  
Hamiltonian Analysis

Abstract Recently a new model has been proposed to describe free massive spin-2 particles in D dimensions in terms of a non symmetric rank-2 tensor eµν and a mixed symmetry tensor Bµ[αβ]. The model is invariant under linearized diffeomorphisms without Stueckelberg fields. It resembles a spin-2 version of the topologically massive spin-1 BF model (Cremmer-Scherk model). Here we apply the Dirac-Bergmann procedure in order to identify all Hamiltonian constraints and perform a complete counting of degrees of freedom. In D = 3 + 1 we find 5 degrees of freedom corresponding to helicities ±2, ±1, 0 as expected. The positivity of the reduced Hamiltonian is proved by using spin projection operators. We have also proposed a parent action that establishes the duality between the Fierz-Pauli and the new model. The equivalence between gauge invariant correlation functions of both theories is demonstrated.

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

scholarly journals Extending the spin projection operators for gravity models with parity-breaking in 3-D

2010 ◽  
Vol 374 (34) ◽  
pp. 3410-3415 ◽  
Author(s):  
C.A. Hernaski ◽  
B. Pereira-Dias ◽  
A.A. Vargas-Paredes
Keyword(s):  
Gravity Models ◽  
Spin Projection ◽  
Projection Operators ◽  
Parity Breaking

Effective Locality QCD calculations and the Gribov copy problem

2020 ◽  
Vol 35 (27) ◽  
pp. 2050230 ◽  
Author(s):  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Field ◽  
Strong Coupling ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Strong Coupling Limit ◽  
Unexpected Result ◽  
Remarkable Property ◽  
Gauge Invariant

Standard functional manipulations have been proven to imply a remarkable property satisfied by the fermionic Green’s functions of QCD and dubbed effective locality. Resulting from a full gauge invariant summation of the gauge field degrees of freedom, effective locality is a non-perturbative property of QCD. This unexpected result has lead to suspect that the famous Gribov copy problem had been somewhat overlooked. It is argued that it is not so. The analysis is conducted in the strong coupling limit, relevant to the Gribov problem.

scholarly journals Random boundary geometry and gravity dual of $$ T\overline{T} $$ deformation

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shinji Hirano ◽  
Masaki Shigemori
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Energy Spectrum ◽  
Correlation Functions ◽  
Degrees Of Freedom ◽  
Dual Language ◽  
Renormalization Group Flow ◽  
Conformal Field ◽  
Logarithmic Corrections ◽  
Group Flow

Abstract We study the random geometry approach to the $$ T\overline{T} $$ T T ¯ deformation of 2d conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $$ T\overline{T} $$ T T ¯ deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of AdS3 spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant $$ T\overline{T} $$ T T ¯ operator. We streamline the method of computation and calculate the energy spectrum and the thermal free energy in a manner that can be directly translated into the gravity dual language. We further generalize this approach to correlation functions and reproduce the all-order result with universal logarithmic corrections computed by Cardy in a different method. In contrast to earlier proposals, this version of the gravity dual of the $$ T\overline{T} $$ T T ¯ deformation works not only for the energy spectrum and the thermal free energy but also for correlation functions.

scholarly journals xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 290 ◽  
Author(s):  
Ivan Agullo ◽  
Javier Olmedo ◽  
Vijayakumar Sreenath
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Computational Algorithm ◽  
Tensor Algebra ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Bianchi I ◽  
Space Formulation

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.

scholarly journals Wind Influence on Miro-launcher Dynamics Model

2019 ◽  
Vol 304 ◽  
pp. 07014
Author(s):  
Teodor-Viorel Chelaru ◽  
Valentin Pana ◽  
Alexandru Iulian Onel ◽  
Tudorel-Petronel Afilipoae ◽  
Andrei Filip Cojocaru ◽  
...  
Keyword(s):  
Atmospheric Turbulence ◽  
Correlation Functions ◽  
Degrees Of Freedom ◽  
Dynamics Model ◽  
Six Degrees Of Freedom ◽  
Body Model ◽  
Rigid Body Model ◽  
Wind Influence ◽  
Three Stages ◽  
Flight Parameters

The paper presents aspects regarding wind influence in dynamics of the three stages micro-launcher. The work is focus on atmospheric turbulence, with dedicated linear model based on characteristics correlation functions, that can be attached to the rigid body model with six degrees of freedom. The results analyzed will be the flight parameters of the launcher, with the wind influence. The novelty of the paper consists in dedicated wind models developed and their implementation in six degrees of freedom micro-launcher model.

scholarly journals Unitarity of Singh-Hagen Model in D Dimensions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Elias L. Mendonça ◽  
R. Schimidt Bittencourt
Keyword(s):  
General Expression ◽  
Spin Projection ◽  
Projection Operators ◽  
Source Terms ◽  
Particle Content ◽  
Complete Set

The particle content of the Singh-Hagen model (SH) in D dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding source terms, we provide a unitarity analysis in D dimensions. In addition, we have also analyzed the positivity of the massless Hamiltonian.

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