scholarly journals A connection between linearized Gauss–Bonnet gravity and classical electrodynamics II: Complete dual formulation

2021 ◽  
pp. 2150030
Author(s):  
Mark Robert Baker
Keyword(s):  
Field Strength ◽  
Gauge Theories ◽  
Equations Of Motion ◽  
Classical Electrodynamics ◽  
Necessary Condition ◽  
Property A ◽  
Gauge Invariant ◽  
Bonnet Gravity ◽  
Dual Formulation ◽  
Higher Spin

In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for [Formula: see text] and linearized Gauss–Bonnet gravity for [Formula: see text]. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in [Formula: see text] can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-[Formula: see text] curvature tensors for all [Formula: see text] are the field strength tensors for each [Formula: see text]. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

scholarly journals GENERATING FUNCTIONAL FOR GAUGE INVARIANT ACTIONS: EXAMPLES OF NONRELATIVISTIC GAUGE THEORIES

2010 ◽  
Vol 25 (10) ◽  
pp. 2087-2101 ◽  
Author(s):  
OLEG ANDREEV
Keyword(s):  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Upper Bound ◽  
Gauge Theories ◽  
Gauge Invariant ◽  
Generating Functional

We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born–Infeld theory, there is an upper bound to the electric field strength in these gauge theories.

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

scholarly journals Exact renormalization group and loop variables: A background independent approach to string theory

2015 ◽  
Vol 30 (32) ◽  
pp. 1530055 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Flat Space ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
String Loop ◽  
Higher Spin ◽  
Exact Renormalization Group

This paper is a self-contained review of the loop variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space–time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.

scholarly journals A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

2019 ◽  
Vol 28 (07) ◽  
pp. 1950092 ◽  
Author(s):  
Mark Robert Baker ◽  
Sergei Kuzmin
Keyword(s):  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Physical Models ◽  
Classical Electrodynamics ◽  
Gauge Invariant ◽  
Bonnet Gravity ◽  
Interesting Connection ◽  
Tensor Potential ◽  
Natural Outcome ◽  
Density Equation

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge-invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives ([Formula: see text]) and a rank of tensor potential ([Formula: see text]), then solving such that the model is completely gauge-invariant (the Lagrangian density, equation of motion and energy–momentum tensor are all gauge-invariant). In the case of [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of [Formula: see text] order of derivatives and [Formula: see text] rank of symmetric tensor potential, linearized Gauss–Bonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized Gauss–Bonnet gravity from a common set of rules provides an interesting connection between two well-explored physical models.

scholarly journals Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities

2021 ◽  
Author(s):  
Mark Robert Baker ◽  
Julia Bruce-Robertson
Keyword(s):  
Unique Solution ◽  
Curvature Tensor ◽  
Gauge Theories ◽  
Classical Electrodynamics ◽  
Gauge Transformations ◽  
Symmetry Properties ◽  
Tensor Potential ◽  
Higher Spin ◽  
Curvature Tensors ◽  
Lagrangian Densities

Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-n field for each spin-n). For this reason they are sometimes referred to as the generalized 'Riemann' tensors. In this article, a method for deriving these curvature tensors from first principles is presented; the derivation is completed without any a priori knowledge of the existence of the Riemann tensors or the curvature tensors of higher-spin gauge theories. To perform this derivation, a recently developed procedure for deriving exactly gauge invariant Lagrangian densities from quadratic combinations of N order of derivatives and M rank of tensor potential is applied to the N = M = n case under the spin-n gauge transformations. This procedure uniquely yields the Lagrangian for classical electrodynamics in the N = M = 1 case and the Lagrangian for higher derivative gravity (`Riemann' and `Ricci' squared terms) in the N = M = 2 case. It is proven here by direct calculation for the N = M = 3 case that the unique solution to this procedure is the spin-3 curvature tensor and its contractions. The spin-4 curvature tensor is also uniquely derived for the N = M = 4 case. In other words, it is proven here that, for the most general linear combination of scalars built from N derivatives and M rank of tensor potential, up to N=M=4, there exists a unique solution to the resulting system of linear equations as the contracted spin-n curvature tensors. Conjectures regarding the solutions to the higher spin-n N = M = n are discussed.

scholarly journals Extended superconformal higher-spin gauge theories in four dimensions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Emmanouil S. N. Raptakis
Keyword(s):  
Gauge Theories ◽  
Conformally Flat ◽  
De Sitter ◽  
Conformal Supergravity ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Higher Spin ◽  
Shell Formulation ◽  
Conserved Currents ◽  
Field Strengths

Abstract Using the off-shell formulation for $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main $$ \mathcal{N} $$ N = 2 results are then generalised to the $$ \mathcal{N} $$ N -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $$ \mathcal{N} $$ N = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $$ \mathcal{N} $$ N = 2 superconformal group.

ON THE QUANTIZATION OF FIELD THEORIES WITH SECOND CLASS CONSTRAINTS

1991 ◽  
Vol 06 (23) ◽  
pp. 2121-2128 ◽  
Author(s):  
R. GIANVITTORIO ◽  
A. RESTUCCIA ◽  
J. STEPHANY
Keyword(s):  
Dynamical Systems ◽  
Gauge Theories ◽  
The Self ◽  
Field Theories ◽  
Gauge Invariant ◽  
Dual Formulation ◽  
Chern Simons

The quantization of a class of dynamical systems subject to second class constraints that allows an analysis in terms of associated gauge theories with first class constraints is discussed. The comparison with early approaches is done. The approach is applied to the self-dual formulation of spin one massive excitations in 3 dimensions. The quantum equivalence to the corresponding gauge invariant Chern–Simons topological massive model is analyzed.

scholarly journals BRST and Superfield Formalism—A Review

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 280
Author(s):  
Loriano Bonora ◽  
Rudra Prakash Malik
Keyword(s):  
Riemannian Geometry ◽  
Gauge Theories ◽  
Original Material ◽  
Comprehensive Description ◽  
Higher Spin ◽  
Gauge Anomalies

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

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.

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