In this paper, a gauge invariant description of massive higher spin bosonic and fermionic particles in frame-like Lagrangian and unfolded formalism in (A)dS${}_4$ is built. A complete set of gauge invariant object is also constructed and the Lagrangian is rewritten in terms of these objects. The unitarity of the theories is studied alongside with the partially massless limits. The calculations are carried out in the multispinor formalism, which simplifies them and is particularly convenient for the supersymmetry studies.
We construct and analyze unfolded off-shell systems for chiral and vector supermultiplets using multispinor formalism and external currents. We find that auxiliary variables of multispinor formalism allow for the interesting reorganization of the unfolded off-shell modules: one can unify dynamical and auxiliary scalars in the Wess-Zumino model, as well as an auxiliary pseudoscalar and a zero-helicity subsector in the vector supermultiplet, so that the resulting unfolded equations get simplified, while various constraints like chirality, electric current conservation and P-oddness of the pseudo…
In this paper we elaborate on higher spin cubic interactions for massless, massive and partially massless fields. We work in the gauge invariant frame-like multispinor formalism, combining Lagrangian and unfolded formulations.
In this paper we construct an unfolded formulation for the massive higher spin N=1 supermultiplets in four dimensional AdS space. We use the same frame-like gauge invariant multispinor formalism that was used previously for their Lagrangian formulation. We also consider an infinite spin limit of such supermultiplets.
We construct a range of supersymmetric cubic vertices for three massless higher spin supermultiplets in the four-dimensional space. We use frame-like multispinor formalism, which allows to avoid most of the technical difficulties and provides a uniform description for bosons and fermions. Our work is based on the so-called Fradkin-Vasiliev formalism for construction of the cubic vertices, which requires the non-zero cosmological constant. Thus we first construct the vertices in AdS space and then consider the flat limit. We show that the AdS supersymmetric vertex is a sum of four elementary ve…
We proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the previous one. The importance of the 4-vector field (and its gauge part) is pointed out.
In this paper we construct a number of cubic interaction vertices for massless bosonic and fermionic higher spin fields in flat four dimensional space. First of all, we construct these cubic vertices in AdS_4 space using a so-called Fradkin-Vasiliev approach, which works only for the non-zero cosmological constant. Then we consider a flat limit taking care on all the higher derivative terms which FV-approach generates. We restrict ourselves with the four dimensions because this allows us to use the frame-like multispinor formalism which greatly simplifies all calculations and provides a descri…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2S+1) theory are found. Next, we proceed to derive the equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation…
We analyze open string vertex operators describing connection gauge fields for spin 3 in Vasiliev's frame-like formalism and perform their extended BRST analysis. Gauge symmetry transformations, generalized zero torsion constraints relating extra fields to the dynamical frame-like field and relation between dynamical frame-like field and fully symmetric Fronsdal's field for spin 3 are all realized in terms of BRST constraints on these vertex operators in string theory. Using the construction, we analyze the 3-point correlator for spin 3 field and calculate Chern-Simons type cubic interactions …
In this paper we develop the frame-like gauge invariant formulation for the massive two-column bosonic fields in (anti) de Sitter space-times. We begin with the partially massless cases in AdS and dS and then we combine these results into the general massive theory. Separate section is devoted to the special case where both columns have equal number of indices.
Till now most of the results on interaction vertices for massless higher spin fields were obtained in a metric-like formalism using completely symmetric (spin-)tensors. In this, the Lagrangians turn out to be very complicated and the main reason is that the higher the spin one want to consider the more derivatives one has to introduce. In this paper we show that such investigations can be greatly simplified if one works in a frame-like formalism. As an illustration we consider massless spin 3 particle and reconstruct a number of vertices describing its interactions with lower spin 2, 1 and 0 o…
We show that 10D spinor helicity formalism can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes. This allows us to develop the spinor helicity formalism for 11D supergravity and a new constrained superfield formalism for 10D SYM and 11D SUGRA amplitudes. We show how the constrained on-shell superfields, one-particle counterparts of the superamplitudes, can be obtained by quantization of massless superparticle mechanics. We make some stages towards the calculation of amplitudes of 10D SYM and 11D SUGRA in this framework. In part…
In this paper we elaborate on the gauge invariant frame-like Lagrangian description for the wide class of the so-called infinite (or continuous) spin representations of Poincaré group. We use our previous results on the gauge invariant formalism for the massive mixed symmetry fields corresponding to the Young tableau with two rows Y(k,l) (Y(k+1/2,l+1/2) for the fermionic case). We have shown that the corresponding infinite spin solutions can be constructed as a limit where k goes to infinity, while l remain to be fixed and label different representations. Moreover, our gauge invariant formalis…
The covariant quantization of massless D=11 superparticle (M0-brane) in its twistor-like Lorentz harmonic formulation is used to clarify the origin and some properties of the Berkovits pure spinor approach to quantum superstring and to search for hidden symmetries of D=11 supergravity. In the twistor like Lorentz harmonic formulation, the SO(16) symmetry is seen already at the classical level. The quantization produces the linearized supergravity multiplet as 128+128=256 component Majorana spinor of SO(16) and also shows an indirect argument in favor of the possible E8 symmetry.
Understanding spin one half is a crucial issue in the De Broglie Bohm framework. In this paper a concrete relativistic realization of spin one half in terms of angular coordinates is developed. A Lagrange formulation is found, equations of motion are derived, and Lorentz invariance is discussed.
Gauge-invariant systems of a general form with higher order derivatives of gauge parameters are investigated within the framework of the BFV formalism. Higher order terms of the BRST charge and BRST-invariant Hamiltonian are obtained. It is shown that the identification rules for Lagrangian and Hamiltonian ghost variables depend on the choice of the extension of constraints from the primary constraint surface.
We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a more general approach for a symplectic formalism, even when there is no Hamiltonian in a canonical sense. We can thus overcome the usual limitations of the canonical quantization, and perform an algebraically consistent quantization for a more general set of Lagrangian systems.
In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field $(A_μ)$ and the (anti-)ghost fields $((\bar C)C)$ of the Lagrangian density of the two $(1 + 1)$-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four $(2 + 2)$-dimensional supermanifold. The long-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields $(\barψ, ψ)$ in the framework of superfield formulation is resolved by a new set of restri…
In the framework of $Sp(2)$ extended Lagrangian field-antifield BV formalism we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.
We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem c…
We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert-Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalis…
The expression of the quantum Ruijsenaars-Schneider Hamiltonian is obtained in the framework of the dynamical $R$-matrix formalism. This generalizes to the case of $U_q(sl_n)$ the result obtained by O. Babelon, D. Bernard and E. Billey for $U_q(sl_2)$ which is the higher difference Lame operator. The general method involved is the universal $R$-matrix construction.
We study the dynamics of classical and quantum particles with spin and dipole moments in external fields within the framework of the general approach by making use of the projection technique. Applications include the neutrino physics in matter, polarization phenomena in astrophysics, high-energy and heavy-ion physics.
We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of …
We establish a new framework of finite temperature field theory for Yang-Mills theories in the physical phase space eliminating all unphysical degrees of freedoms. Relating our method to the imaginary time formalism of James and Landshoff in temporal axial gauge, we calculate the two-loop pressure and provide a systematic and unique method to construct the additional vertices encountered in their approach.
We consider gaugeon formulations which discuss the quantum gauge freedom covariantly in the framework of generalized BRST transformation for the Yang-Mills theory as well as the BRST invariant Higgs model. We generalize the BRST symmetries of both the Yang-Mills theory and the Higgs model by making the transformation parameter finite and field-dependent. Remarkably, we observe that the gaugeon Lagrangian which describe the quantum gauge freedom appear automatically in the effective theories along with the natural shift in gauge parameters under specific finite field-dependent parameters.
In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalized gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism which embeds more acceptable Kugo-Ojima subsidiary condition. Further, the BRST symmetry is made finite and field-dependent. Remarkably, the Jacobian of path integral under finite and…
We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $λϕ^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on the solution of the classical equation of motion for the field, and Gaussian fluctuations around it. Our result is non-perturbative and differs from the standard one-loop effective potential for field values larger than $T/\sqrtλ$.
Recently there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system which is generally out of equilibrium, is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up to $\hat{\mathbf{O}}(\hbar)$ order. In particular, we clarify certain subtle a…
We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scala…
The D=10 pure spinor constraint can be solved in terms of spinor moving frame variables and 8-component complex null vector which can be related to the kappa-symmetry ghost. Using this and similar solutions for the conjugate pure spinor and other elements of the non-minimal pure spinor formalism we present a (hopefully useful) reformulation of the measure of the pure spinor path integral for superstring in terms of products of Cartan form corresponding to the coset of 10D Lorentz group and to the coset of complex orthogonal group SO(8,C). Our study suggests a possible complete reformulation of…
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
We study the gravitational dynamics in the early inspiral phase of coalescing compact binaries using Non-Relativistic General Relativity (NRGR) - an effective field theory formalism based on the post-newtonian expansion, but which provides a consistent lagrangian framework and a systematic way in which to study binary dynamics and gravitational wave emission. We calculate in this framework the spin-orbit correction to the newtonian potential at 2.5 PN.
Herein we propose a new numerical technique for solving field theories: the large momentum frame (LMF). This technique combines several advantages of lattice gauge theory with the simplicity of front form quantisation. We apply the LMF on QED(1+1) and on the $ϕ^4(3+1)$ theory. We demonstrate both analytically and in practical examples (1) that the LMF does neither correspond to the infinite momentum frame (IMF) nor to the front-form (FF) (2) that the LMF is not equivalent to the IMF (3) that the IMF is unphysical since it violates the lattice scaling window and (4) that the FF is even more unp…
The present work contains a complete formulation of the Batalin-Vilkovisky (BV) formalism in the framework of locally covariant field theory. In the first part of the thesis the classical theory is investigated with a particular focus on the infinite dimensional character of the underlying structures. It is shown that the use of infinite dimensional differential geometry allows for a conceptually clear and elegant formulation. The construction of the BV complex is performed in a fully covariant way and we also generalize the BV framework to a more abstract level, using functors and natural tra…
Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.
In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of $k$-contact Hamiltonian systems, which is based on the $k$-symplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner--Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incor…
