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A gauge theory of solids with conformal symmetry is formulated to model various electromechanical and magnetomechanical coupling phenomena. If the pulled back metric of the current configuration (the right Cauchy-Green tensor) is scaled with a constant, the volumetric part of the Lagrange density changes while the isochoric part remains invariant. However, upon a position dependent scaling, the isochoric part also loses invariance. In order to restore the invariance of the isochoric part, a 1-form compensating field is introduced and the notion of a gauge covariant derivative is utilized to minimally replace the Lagrangian. In view of obvious similarities with the Weyl geometry, the Weyl condition is imposed through the Lagrangian and a minimal coupling is employed so the 1-form could evolve. On deriving the Euler-Lagrange equations based on the action functional, we observe a close similarity with the governing equations for flexoelectricity under isochoric deformation if the exact part of 1-form is interpreted as the electric field and the anti-exact part as the polarization vector. Next, we model piezoelectricity and electrostriction phenomena by contracting the Weyl condition in various ways. Applying the Hodge decomposition theorem on the 1-form which leads to the curl of a pseudo-vector field and a vector field, we also model magnetomechanical phenomena. Identifying the pseudo-vector field with magnetic potential and the vector part with magnetization, flexomagnetism, piezomagnetism and magnetostriction phenomena under isochoric deformation are also modeled. Finally, we consider an analytical solution of the equations for piezoelectricity to provide an illustration on the insightful information that the present approach potentially provides., Comment: 46 pages, 1 figure

Recently, Antoniadis, Konitopoulos and Savvidy introduced, in the context of the so-called extended gauge theory, a procedure to construct background-free gauge invariants, using non-abelian gauge potentials described by higher degree forms.In this article it is shown that the extended invariants found by Antoniadis, Konitopoulos and Savvidy can be constructed from an algebraic structure known as free differential algebra. In other words, we show that the above mentioned non-abelian gauge theory, where the gauge fields are described by p-forms with p≥2, can be obtained by gauging free differential algebras.

The problem of the gauge dependence of the effective field is considered within the framework of the method of the functional renormalization group for general gauge theories.

We prove global existence of solution to space-time monopole equations in one space dimension under the spatial gauge condition A1=0 and the temporal gauge condition A0=0.

I report the reason why Tensor satisfying Binary Law has relations toward physics in this article. Q: The n th-order covariant derivative of the Vector {Aμ, Aμ}:(n=1) satisfying Binary Law. R: The n th-order covariant derivative of the Vector {Aμ, Aμ}:(n≥2) satisfying Binary Law. I have reported in other articles about Q. I report R in this article. I obtained the following results in this. I got the conclusion that derived function became 0. The derived function becoming 0 in the n th-order covariant derivative of the covariant vector Aμ here in the case of n=2. Similarly, in the n th-order covariant derivative of the contravariant vector Aμ in the case of n=4 .

We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal gauge fields subject to the invariant equations. Our approach gives a manifestly conformal and gauge covariant formulation for these fields. Although such formulation employs numerous auxiliary fields, it comes with a systematic procedure for their elimination that results in a more concise formulation involving only a reasonable set of auxiliaries, which eventually (at least in principle) can be reduced to the minimal formulation in terms of the irreducible Lorentz tensors. The simplest mixed-symmetry field, namely, the rank-3 tensor associated to the two-row Young diagram, is considered in some details., Comment: 29 pages, v2: minor corrections, references added, to appear in Nucl. Phys. B

First, covariance is explained. Then, the relation between covariant derivative and tensor analysis is described. The role of covariant derivative in local gauge invariance is given. The applications of gauge covariant derivative for sound propagation in continuous fluids and for sound propagation in solids are provided.

The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description: on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.

In this article, we introduce a discrete definition of connection on simplicial manifolds, involving closed-form continuous expressions within simplices and finite rotations across simplices. The finite-dimensional parameters of this connection are optimally computed by minimizing a quadratic measure of the deviation to the (discontinuous) Levi-Civita connection induced by the embedding of the input triangle mesh, or to any metric connection with arbitrary cone singularities at vertices. From this discrete connection, a covariant derivative is constructed through exact differentiation, leading to explicit expressions for local integrals of first-order derivatives (such as divergence, curl, and the Cauchy-Riemann operator) and for L 2 -based energies (such as the Dirichlet energy). We finally demonstrate the utility, flexibility, and accuracy of our discrete formulations for the design and analysis of vector, n -vector, and n -direction fields.

This paper reports the new progresses in the axiomatization of tensor analysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentiations. These progresses strengthen the tendency of the axiomatization of tensor analysis.

We study partially massless gravity theory(PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self interaction terms necessarily breaks the $U(1)$ gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, $\mathcal L_{int}\sim h_{\mu\nu}T^{\mu\nu}$, where $h_{\mu\nu}$ is the PM gravity field and $T^{\mu\nu}$ is the stress-energy tensor of the matter fields. To retain the $U(1)$ gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be non-local in this case. The second type interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom. 2 of them are traceless tensor modes and they are light like fields. The other 2 are transverse vector modes and their dispersion relation changes as background space time (de Sitter) evolutes. In the very early time, they are light like but in the very late time, their velocity become a half of speed of light. The vector mode dispersion relation shows momentum dependent behavior. In fact, the higher(lower) frequency modes show the faster(slower) velocity. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators., Comment: 31+1 pages. A new subsection is added, a few paragraphs in introduction are added and several references are added. A few typos are corrected

International audience; Gauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be met by essentially finding a way to effectively reduce gauge symmetries. We propose a review of a way to do so which we call the dressing field method. We show how the BRST algebra satisfied by gauge fields, encoding their gauge transformations, is modified. We outline noticeable applications of the method, such as the electroweak sector of the Standard Model and the local twistors of Penrose.

This paper further extends the generalized covariant derivative from the first covariant derivative to the second one on curved surfaces. Through the linear transformation between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the second class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric structure of the tensor analysis on curved surfaces are revealed.

This paper extends the classical covariant derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form invariability. Based on the generalized covariant derivative, a covariant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analysis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

We continue earlier discussions on the exact renormalization group and loop variables on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motion - this is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space time curvature of the (arbitrary) background is zero. The exact RG equations give quadratic equations of motion for all the modes {\em including} the physical graviton. The level $(2,\bar 2)$ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory., 41 pages

Recently we introduced an extended vector bundle X on which non-Abelian tensor gauge fields realize a connection. Our aim here is to introduce interaction of these non-Abelian tensor gauge fields with fermions and bosons. We have found that there exist two series of gauge invariant forms describing this interaction. The linear sum of these forms comprises the general gauge invariant Lagrangian. Studying the corresponding Euler-Lagrange equations we found that a particular linear combination of these forms exhibits enhanced symmetry which guarantees the conservation of the corresponding high-rank currents. A possible mechanism of symmetry breaking and mass generation of tensor gauge bosons is suggested., 18 pages, LaTex file

Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been acknowledged for quite some time that boundaries can break gauge invariance, and thereby turn gauge degrees of freedom into physical ones. There is however no known systematic way of identifying these degrees of freedom and possible associated boundary observables. Following recent work by Donnelly and Freidel, we show that this can be achieved by extending the covariant Hamiltonian formalism so as to make it gauge-invariant under arbitrary large gauge transformations. This can be done at the expense of extending the phase space by introducing new boundary fields, which in turn determine new boundary symmetries and observables. We present the general framework behind this construction, and find the conditions under which it can be applied to an arbitrary Lagrangian. By studying the examples of Abelian Chern-Simons theory and first order three-dimensional gravity, we then show that the new boundary observables satisfy the known corresponding Kac-Moody affine algebras. This shows that this new extended phase space formulation does indeed properly describe the dynamical boundary degrees of freedom, and gives credit to the results which have been previously derived in the case of diffeomorphism symmetry. We expect that this systematic understanding of the boundary symmetries will play a major role for the quantization of gravity in finite regions., Published version

We perform a complete and systematic calculation of the octet-baryon form factors within the fully covariant approach of SU(3) chiral perturbation theory at O(p^3). We use the extended on-mass shell renormalization scheme, and include explicitly the vector mesons and the spin-3/2 decuplet intermediate states. Comparing these predictions with data including magnetic moments, charges, and magnetic radii, we determine the unknown low-energy constants, and give predictions for yet unmeasured observables, such as the magnetic moment of the Sigma^0, and the charge and magnetic radii of the hyperons., Accepted for publication in Phys. Rev. D

Local or gauge symmetries are fundamental in elementary-particle physics to describes electroweak and strong interactions in the standard model. The gauge symmetry underlies the dynamics and is employed to describe the interaction between fields. For obtaining a gauge-invariant Lagrangian, the gauge-covariant derivative is defined such that any gauge fields are associated with the generators of the local symmetry group. In this paper, we obtain the gauge-covariant derivative and the gauge-invariant Lagrangian density in de Sitter ambient space formalism.

In this note we make a review of the concepts of connection and covariant derivative on modules, in a purely algebraic context. Throughout the text, we consider algebras over an algebraically closed field of characteristic 0 and module will always mean left module. First, we concentrate our attention on a k-algebra A which is commutative, and use the Kahler differentials module, Ω¹A/k, to define connection (see Subsection 2.1). In this context, it is verified that the existence of connections implies the existence of covariant derivatives (cf. Prop. 2.3), and that every projective module admits a connection (cf. Prop. 2.5). Next (in Section 3), we focus our attention in the discussion of some counterexamples comparing these two notions. In fact, it is known that these two notions are equivalent when we consider regular k-algebras of finite type (see [18], Prop. 4.2). As well as, that there exists a connection on M if, and only if, the Atiyah-Kodaira-Spencer class of M, c(M), is zero (see [17] , Prop. 4.3). Finally, we take into account the case where A is (not necessarily commutative) and it is used the bimodule, Ω¹, of noncommutative differentials introduces by Connes [9], [10] in place of Kahler differentials to define a connection. In this case, it is proven that a module admits such connection if, and only if, it is a projective module (see [25], Theorem 5.2).

In the literature one can find two different expressions for the gauge-field propagator in light-cone gauge, containing the sum of three rather than two terms. The question of which of the two is the correct one has been a subject of debate. We propose a solution to this question by evaluating one-loop level processes in QED, both in the covariant approach in the light-cone gauge and in the light-front time-ordered perturbation theory (TOPT) approach, proving the equivalence between the two formulations of the theory. The form of the propagator turns out to be crucial in the proof, in particular as concerns its relation with the diagrams containing instantaneously propagating photons and instantaneous interactions. We show that the diagrams in light-front TOPT with instantaneous photons can be recovered in the covariant approach starting from the propagators with only two terms. Our proof of the equivalence clarifies which form should be used for the gauge-field propagator in the covariant approach. This result naturally applies to the QCD case also.

The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a non-trivial Polyakov loop to the pressure of the gluon plasma. The correct subtraction of the vacuum contribution in the free action density is argued for. The Poisson resummed expression for the pressure can be evaluated analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at $T \to \infty$, while the limit $T \to 0$ is afflicted by artifacts due to massless modes in the confined phase. Several remedies to remove these artifacts are discussed. Using the numerical $T=0$ solutions for the ghost and gluon propagators in the covariant variational approach as input, the pressure, energy density and interaction strength are calculated and compared to lattice data., Comment: 25 pages, 16 pdf figures, pdflatex; fixed a missing factor in the free energy; revised parts of section 4 and 5; added 4 references

We introduce a covariant Lorentz force written in terms of the newly formed 4-potential vector. We show that it satisfies the established constraints: it is a spacelike 4-vector and it is 4-orthogonal to the 4-velocity. The 0th component of the Lorentz 4-force is recognized as describing the energy transfer from the electromagnetic-field to the particle motion. We next seek a covariant variation-principle. Several approaches are seen in literature: A) the non-covariant relativistic generalization of the usual three dimensional action; B) the covariant generalization based on particle proper time as the evolution parameter; C) a variation of the particle proper times, making it a part of dynamics for the kinetic energy only; and D) we also describe an extension of the case to be fully consistent, with both kinetic and potential terms in the action treated in the same fashion. These different approaches attempt to resolve in different fashions the need to implement the constraint \(c^{2}=u^{2}\) which reduced the number of independent velocity components. An approach that avoids this difficulty was proposed long ago, but in essence was lost in literature; we reintroduce this Hamiltonian-like 4-dimensional alternative based on a mass-function.

In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use to probe the pole structure of the massive gauge boson in a gauge invariant fashion., Comment: 31 pages. v2: extended bibliography + new subsection on LKF transformations

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_{a}$-potential parameters $\lambda_{a}=s_{a}\Lambda$ induced by a finite even-valued functional $\Lambda$ and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary $R_{\xi }$-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h$, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST\ transformations to the case of general gauge theories and present an ansatz for such transformations., Comment: 31 pages, no figures, misprint in the Eq. (5.1) corrected

We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether’s theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether’s theorem (Struckmeier and Reichau, Exciting Interdisciplinary Physics, Springer, New York, p. 367, 2013, [1]). The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the respective Hamiltonian.

In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs., 8 pages, no figure. Due to the constructive contribution of X. Bekaert in this letter, his name is added as a new author. This version of the paper accepted for publication in PLB(2016)

By explicit calculations of four-field couplings, we observe that the higher derivative corrections to the DBI action in flat space-time, can be either in a covariant form or in a T-duality invariant form. The two forms are related by a non-covariant field redefinition. Using this observation, we then propose a non-covariant but T-duality invariant action which includes all orders of massless fields and has two extra derivatives with respect to the DBI action., Comment: 16 pages, latex file, no figure; v3:minor modification, it appears in NPB

The recently derived expressions for finite gauge transformations in double field theory with duality group O(d,d) are generalised to give expressions for finite gauge transformations for extended field theories with duality group SL(5,R), SO(5,5) and E6. The generalised metrics are discussed., 24 pages

The third method we shall consider for numerical QED calculations on bound states is the Covariant-Evolution operator (CEO), developed during the last decade by the Gothenburg group (Lindgren et al., Phys. Rep. 389, 161–261, 2004) [130], (Lindgren et al., Can. J. Phys. 83, 183–218, 2005) [131], (Lindgren et al., Phys. Rev. A 73, 062–502, 2006) [132]. This procedure is based upon the non-relativistic time-evolution operator, discussed in Chap. 3, but made relativistically covariant in order to be applicable in relativistic calculations. This method has the advantage over the two methods discussed previously, the S-matrix procedure and the Green’s-function procedure, that it can be used perturbatively, and the perturbations can be included in the wave function—not only added to the energy. It then forms a convenient basis for a covariant relativistic many-body perturbation procedure, where electron correlation and quantum electrodynamics are systematically combined. For two-electron systems this is fully compatible with the Bethe–Salpeter equation. This question will be the main topic for the rest of the book.

We discuss the equivalence between light-front time-ordered-perturbation theory and covariant quantum field theory in light-front quantization, in the case of quantum electrodynamics at one-loop level. In particular, we review the one-loop calculation of the vertex correction, fermion self-energy and vacuum polarization. We apply the procedure of integration by residue over the light-front energy in the loop to show how the perturbative expansion in covariant terms can be reduced to a sum of propagating and instantaneous diagrams of light-front time-ordered perturbation theory. The detailed proof of equivalence between the two formulations of the theory resolves the controversial question on which form should be used for the gauge-field propagator in the light-cone gauge in the covariant approach., Comment: 18 pages, 5 figures

In this note we continue to pursue the question whether gauge theories can be represented in terms of effective "scalar" degrees of freedom. We provide such a consistent representation for a free photon theory in 3+1 dimensions. Building on results of [1] we construct a Lagrangian with a four derivative kinetic term, and demonstrate that despite seeming nonlinearity of the theory it is equivalent to a theory of a free photon., 7 pages

We combine symmetry structures of ordinary (parallel directions) and dual (transversal directions) coordinates to construct the Dirac-Born-Infeld (DBI) theory. The ordinary coordinates are associated with the Neumann boundary conditions and the dual coordinates are associated with the Dirichlet boundary conditions. Gauge fields become scalar fields by exchanging the ordinary and dual coordinates. A gauge transformation of a generalized metric is governed by the generalized Lie derivative. The gauge transformation of the massless closed string theory gives the $C$-bracket, but the gauge transformation of the open string theory gives the $F$-bracket. The $F$-bracket with the strong constraints is different from the Courant bracket by an exact one-form. This exact one-form should come from the one-form gauge field. Based on symmetry point of view, we deduce a suitable action with a non-zero $H$-flux at the low-energy level. From an equation of motion of the scalar dilaton, it defines a generalized scalar curvature. Finally, we construct a double sigma model with a boundary term and show that this model with constraints is classically equivalent to the ordinary sigma model., Comment: 30 pages, minor changes

A procedure for energy-dependent perturbation expansion has been developed, based upon the covariant evolution operator method. This makes it possible to treat energy-dependent perturbations very much like the energy-independent ones in standard many-body perturbation theory. This has been applied to the non-radiative QED perturbations (retardation and virtual electron–positron pairs) as well as the radiative ones (electron self-energy, vacuum polarization and vertex correction). The combination of QED and electron correlation, beyond two-photon exchange, has been evaluated, using the Coulomb gauge. It turned out that in that gauge the extremely time-consuming model-space contributions of the self-energy and vertex corrections do not have to be evaluated in full. In the Feynman gauge no sensible results could be obtained in this way, as is demonstrated by the numerical results.

We show that there exists a representation of a matrix valued gauge field via intrinsic "BRST" operator assigned to matrix valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang - Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators., 15 pages, no figures, Section 6 extended with (6.14), (6.15); v3: Section 7 added, minor corrections; v4: Section 4, minor corrections; v5: formula (4.11) modified

We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge., 8 pages. v2: version accepted for publication in PhysRevD

We compute the gluon and ghost propagators of Yang-Mills theory in linear covariant gauges from the coupled system of Dyson-Schwinger equations. For small values of the gauge fixing parameter $\xi\sim 0.1$, the deviations to the Landau gauge already become clearly visible. For the ghost dressing function, this is reflected in a logarithmic infrared suppression. Also, the gluon dressing function changes - but only quantitatively - and the gluon propagator remains finite at zero momentum. From the results, a running coupling is extracted., Comment: 9 pages, 3 figures, agrees with version published in PRD

We extend the covariant variational approach for SU(N) Yang-Mills theory in Landau gauge to non-zero temperatures. The renormalization of the zero-temperature case is revisited and it is shown that the same counterterms are sufficient to render the low-order Green's function finite at non-zero temperature. We compute the ghost and gluon propagator numerically and show that it agrees in all qualitative respects with the results of high-precision lattice calculations., pdflatex, 36 pages, 10 pdf figures

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle., Comment: 37 pages

Properties of the functional classes of star-product elements associated with higher-spin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra ${\mathcal H}$, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed., 25 pages; V2: The version to appear in JHEP, typos corrected, a comment in Section 6 added

Canonical analysis of 3-D Poincare gauge gravity actions yield symmetries that seem quite different from the underlying Poincare symmetry. Though both symmetries are themselves off-shell, it has been noted in literature that the two become equivalent only on-shell. But then, two inequivalent sets of complete symmetries for the same action are physically untenable and will need more independent primary first-class constraints than are available. We report a resolution of this discrepancy by showing that the hamiltonian and Poincare symmetries are canonically equivalent to each other, being related through trivial gauge transformations.