scholarly journals Massless spin 3/2 field, spherical solutions, eliminating of the gauge degrees of freedom

2021 ◽  
Vol 65 (6) ◽  
pp. 668-679
Author(s):  
A. V. Ivashkevich ◽  
E. M. Ovsiyuk ◽  
V. V. Kisel ◽  
V. M. Red’kov
Keyword(s):  
Degrees Of Freedom ◽  
General Structure ◽  
General System ◽  
Field Function ◽  
Radial Functions ◽  
Recurrent Relations ◽  
Massless Spin ◽  
Independent Functions ◽  
Component Field ◽  
Rank 2

Relativistic system for a vector-bispinior describing a massless spin 3/2 field is studied in the spherical coordinates of Minkowski space. Presentation of the equation with the use of the covariant Levi-Civita tensor exhibits existence of the gauge solutions in the form of the covariant 4-gradient of an arbitrary bispinor. Substitution for 16-component field function is based on the use of Wigner functions, it assumes diagonalization of the operators of energy, square and third projection of the total angular momentum, and space reflection. We derive radial system for eight independent functions. General structure of the spherical gauge solutions is specified, and it is demonstrated that the gauge radial functions satisfy the derived system. It is proved that the general system reduces to two couples of independent 2-nd order and nonhomogeneous differential equations, their particular solutions may be found with the use of the gauge solutions. The corresponding homogeneous equations have one the same form, they have three regular singularities and one irregular of the rank 2. Frobenius types solutions for this equation have been constructed, and the structure of the involved power series with 4-term recurrent relations sre studied. Six remaining radial functions may be straightforwardly found by means of the simple algebraic relations. Thus, we have constructed two types of solutions with opposite parities which do not contain gauge constituents.

Generalized Hamiltonian dynamics

1958 ◽  
Vol 246 (1246) ◽  
pp. 326-332 ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Hamiltonian Formalism ◽  
Direct Solution ◽  
Independent Functions

The author’s procedure for passing from the Lagrangian to the Hamiltonian when the momenta are not independent functions of the velocities is put into a simpler and more practical form, the main results being obtained by a direct solution of the equations provided by the consistency requirements. It is shown how, under certain conditions, one can eliminate some of the degrees of freedom and so make a substantial simplification in the Hamiltonian formalism.

Homogeneous variables in classical dynamics

1933 ◽  
Vol 29 (3) ◽  
pp. 389-400 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Degrees Of Freedom ◽  
Scalar Potential ◽  
Rest Mass ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Lagrangian Function ◽  
Practical Case ◽  
Classical Dynamics ◽  
Hamiltonian Method ◽  
Independent Functions

The well-known methods of classical mechanics, based on the use of a Lagrangian or Hamiltonian function, are adequate for the treatment of nearly all dynamical systems met with in practice. There are, however, a few exceptional cases to which the ordinary methods are not immediately applicable. For example, the ordinary Hamiltonian method cannot be used when the momenta pr, defined in terms of the Lagrangian function L by the usual formulae pr = ∂L/∂qr, are not independent functions of the velocities. A practical case of this kind is provided by the electromagnetic field, considered as a dynamical system with an infinite number of degrees of freedom, since the momentum conjugate to the scalar potential at any point vanishes identically. Again, for the very simple example of the relativistic motion of a particle of zero rest-mass in field-free space, the Lagrangian function vanishes and the usual Lagrangian method is not applicable.

Symplectic geometry of radiative modes and conserved quantities at null infinity

1981 ◽  
Vol 376 (1767) ◽  
pp. 585-607 ◽  
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Space ◽  
Degrees Of Freedom ◽  
Symplectic Geometry ◽  
Conserved Quantities ◽  
Null Infinity ◽  
Hamiltonian Description ◽  
Infinite Dimensional ◽  
Massless Spin

The Hamiltonian description of massless spin zero- and one-fields in Minkowski space is first recast in a way that refers only to null infinity and fields thereon representing radiative modes. With this framework as a guide, the phase space of the radiative degrees of freedom of the gravitational field (in exact general relativity) is introduced. It has the structure of an infinite-dimensional affine manifold (modelled on a Fréchet space) and is equipped with a continuous, weakly non-degenerate symplectic tensor field. The action of the Bondi-Metzner-Sachs group on null infinity is shown to induce canonical transformations on this phase space. The corresponding Hamiltonians – i. e. generating functions – are computed and interpreted as fluxes of supermomentum and angular momentum carried away by gravitational waves. The discussion serves three purposes: it brings out, via symplectic methods, the universality of the interplay between symmetries and conserved quantities; it sheds new light on the issue of angular momentum of gravitational radiation; and, it suggests a new approach to the quantization of the ‘true’ degrees of freedom of the gravitational field.

UNIFIED ELECTROWEAK MODEL BASED ON SPACE–TIME AND ISOSPIN SYMMETRIES

2005 ◽  
Vol 20 (01) ◽  
pp. 175-198 ◽  
Author(s):  
D. SPEHLER ◽  
G. C. MARQUES
Keyword(s):  
Degrees Of Freedom ◽  
Space Time ◽  
Scalar Particles ◽  
Symmetry Breakdown ◽  
Vector Bosons ◽  
Rank 2 ◽  
Electroweak Model ◽  
Spontaneous Symmetry Breakdown ◽  
Internal Degrees Of Freedom

We propose a spinorial approach to the unified electroweak interactions, in which no use is made of spontaneous symmetry breakdown. No scalar particles are needed in order to break the symmetry. No reference is made to gauge symmetry. Our approach stresses the role of space–time and isospin symmetries in the build up of the electroweak model. Internal degrees of freedom, such as isospin, are incorporated in the theory by using spinors carrying isospin indices. All vector bosons are described by a rank 2 field in the spinorial and the isospinorial indices. Leptons are accomodated in a rank 1 spinor field and in a rank 2 isospin field as well. The dynamical variables of the theory are the chiral and isochiral components of these fields.

scholarly journals Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, $$ \mathcal{N} $$ = 1 superspace

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
S. James Gates ◽  
Yangrui Hu ◽  
S.-N. Hazel Mak
Keyword(s):  
Computational Efficiency ◽  
Degrees Of Freedom ◽  
Component Decomposition ◽  
Physics Literature ◽  
Fermionic Fields ◽  
Component Field ◽  
Scalar Superfield ◽  
First Time

Abstract For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, $$ \mathcal{N} $$ N = 1 superfield supergravity. We find the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.

SEPARATION OF ROTATIONAL DEGREES OF FREEDOM IN A QUANTUM THREE-BODY PROBLEM

2001 ◽  
Vol 10 (01) ◽  
pp. 69-82 ◽  
Author(s):  
XIAO-YAN GU ◽  
BIN DUAN ◽  
ZHONG-QI MA
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Three Body Problem ◽  
Radial Functions ◽  
Base Functions ◽  
Rotational Degrees Of Freedom ◽  
Three Body ◽  
The Given

We demonstrate explicitly how the rotational degrees of freedom in a quantum three-body problem is separated completely from the internal ones. It is shown that only finite partial angular momentum states are involved in constructing the base-functions with the given angular momentum and parity, and the contributions by the remaining partial angular momentum states are incorporated into the contributions by the generalized radial functions.

scholarly journals A Chargeless Complex Vector Matter Field in Supersymmetric Scenario

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
L. P. Colatto ◽  
A. L. A. Penna
Keyword(s):  
Degrees Of Freedom ◽  
Mass Shell ◽  
Equations Of Motion ◽  
Matter Field ◽  
Complex Vector ◽  
Massive Vector ◽  
Spinor Fields ◽  
Respective Field ◽  
Component Field ◽  
Matter Fields

We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a globalU1gauge symmetry. For the aim of dealing with consistent terms without breaking the globalU1symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.

scholarly journals NDF of the near-field of a strip source in orthogonal directions

2020 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Inverse Problems ◽  
Closed Form ◽  
Degrees Of Freedom ◽  
Near Field ◽  
Closed Form Expression ◽  
Main Difficulty ◽  
Form Expression ◽  
Independent Functions ◽  
Near Zone

<div><div>In the manuscript, we address the problem of evaluating the</div><div>number of degrees of freedom (NDF) of the field radiated by a strip source along all the directions orthogonal to it. </div><div>The NDF represents at the same time the number of independent functions required to represent the data with a given degree of accuracy, and the dimension of the unknowns subspace that can be stably reconstructed. For such reason, the knowledge of the NDF gives insight on the forward and on the inverse problems and it represents one of the metrics to evaluate the achievable performance in the inversion.</div></div><div>The main difficulty arises since in near-zone the eigenvalue</div><div>problem that must be solved for the computation of the NDF,</div><div>involves a non-convolution and non-bandlimited kernel. In the paper, we show how to overcome this drawback and how to obtain a closed-form expression of the NDF which highlights the role played by the configuration parameters.</div>

scholarly journals Positive Returns and Equilibrium: Simultaneous Feedback Between Public Opinion and Social Policy

2018 ◽  
Author(s):  
Nate Breznau
Keyword(s):  
Public Opinion ◽  
Social Policy ◽  
Degrees Of Freedom ◽  
Small Body ◽  
General System ◽  
Stable Set ◽  
Future Research ◽  
Cross Sectional ◽  
Policy System ◽  
Cross National

This paper pushes forward political research from across disciplines seeking to understand the linkages between public opinion and social policy in democracies. It considers the thermostatic and the increasing returns perspectives as pointing toward a potentially stable set of effects running between opinion and policy. Both theoretical perspectives argue that opinion and policy are reciprocally causal, feeding back on one another. This is a general argument found in opinion-policy literatures. However, much empirical research claims to model “feedback” effects when actually using separate unidirectional models of opinion and policy. Only a small body of research addresses opinion-policy endogeneity directly. In this paper I consider an opinion-policy system with simultaneous feedback and without lags. I argue that there is a theoretical equilibrium in the relationship of opinion and policy underlying the otherwise cyclical processes that link them. Given that available cross-national data are cross-sectional and provide limited degrees of freedom, an ideal theoretical model must be somewhat constrained in order to arrive at empirically meaningful results. In this challenging and exploratory undertaking I hope to open up the possibility of a general system of effects between public opinion and social policy and how to model them in future research. I focus on social welfare policy as it is highly salient to public interests and a costly area of government budgets, making it an area of contentious policymaking. Social policy is also a major part of the thermostatic model of opinion and policy, which was recently extended to the cross-national comparative context (Wlezien &amp; Soroka, 2012) providing a critical predecessor to this paper because identification of equilibrium between public opinion and social policy in any given society is greatly enhanced through comparison with other societies. This counterfactual approach helps to identify opinion-policy patterns that may not change much within societies, but can be seen as taking on discrete trajectories between societies.

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.

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