Physical Degrees Of Freedom Research Articles

Hamiltonian formulation of the linearized hypersurface-orthogonal Einstein-aether theory

We perform the Hamiltonian formulation of the Einstein-aether theory subject to the condition of hypersurface-orthogonality on the aether vector. Our main aim is to obtain the bulk Hamiltonian together with its constraints and their algebra. We implement a perturbative approach, studying the theory at the linearized level. Under the condition of hypersurface orthogonality the aether vector can be represented by a scalar field. The theory has two first-class constraints, which are associated to the symmetry of general diffeomorphisms over the spacetime. One of the constraints depends on the perturbative aether field, generating linear-order diffeomorphisms on it. We also present the reduced bulk Hamiltonian depending on the physical degrees of freedom. We find conditions on the coupling constants enusring the positiveness of the reduced Hamiltonian and the hyperbolicity of the propagation equations of the independent modes.

Cosmic time and reduced phase space of general relativity

In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in General Relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein's theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly by imposing transversality. The theorems of Maskawa-Nishijima appositely relate the reduced phase space to the physical variables in canonical functional integral and Dirac's criterion for second class constraints to nonvanishing Faddeev-Popov determinants in the phase space measures. A reduced physical Hamiltonian for intrinsic time evolution of the two physical d.o.f. emerges. Freed from the first class Dirac algebra, deformation of the Hamiltonian constraint is permitted, and natural extension of the Hamiltonian while maintaining spatial diffeomorphism invariance leads to a theory with Cotton-York term as the ultraviolet completion of Einstein's theory.

Gauge symmetry and constraints structure for topologically massive AdS gravity: a symplectic viewpoint

By applying the Faddeev–Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant Lambda , elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via a suitable partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev–Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.

Dynamical structure of Carrollian Electrodynamics

We present an action of ultra-relativistic electrodynamics on a flat Carroll manifold. The model exhibits a couple of physical degrees of freedom per space-point. We observe that the action of the conformal Carroll algebra on the phase space is Hamiltonian in 4 space-time dimensions. Moreover the elements of the algebra give rise to an infinite number of conserved charges and the charge algebra is an exact realization of the kinematical algebra.

Fakeons and Lee-Wick models

The “fakeon” is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we study the fakeon models, that is to say the theories that contain fake and physical degrees of freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. We investigate the properties of arbitrary Feynman diagrams and, among other things, prove that the fakeon models are perturbatively unitary to all orders. If standard power counting constraints are fulfilled, the models are also renormalizable. The S matrix is regionwise analytic. The amplitudes can be continued from the Euclidean region to the other regions by means of an unambiguous, but nonanalytic, operation, called average continuation. We compute the average continuation of typical amplitudes in four, three and two dimensions and show that its predictions agree with those of the nonanalytic Wick rotation. By reconciling renormalizability and unitarity in higher-derivative theories, the fakeon models are good candidates to explain quantum gravity.

Polynomial spectrum of gamma ray from dark matter

In this paper, we present some general features of gamma-ray spectra from dark matter (DM). We find that the spectrum with sharp features could appear in a wide class of DM models and mimic the gamma line signals. If all other physical degrees of freedom are heavy or effectively decoupled, the resulting gamma ray from DM decay or annihilation would generally have polynomial-type spectra or power-law with positive index. We illustrate our findings in a model-independent framework with generic kinematic analysis. Similar results can also apply for cosmic ray or neutrino cases.

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on “seed” scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.

Gravity with free initial conditions: A solution to the cosmological constant problem testable by CMB B -mode polarization

In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a motivation to solve the cosmological constant problem. This was done by setting four constraints on metric variations in the action principle, which is reasonable because the gravity's physical degrees of freedom are at most six. However, there are two problems about this theory; the three constraints in addition to the unimodular condition were introduced without clear physical meanings, and the flat Minkowski spacetime is unstable against perturbations. Here a new set of gravitational field equations is derived by replacing the three constraints with new ones requiring that geodesic paths remain geodesic against metric variations. The instability problem is then naturally solved. Implications for the cosmological constant $\Lambda$ are unchanged; the theory converges into EFE with nonzero $\Lambda$ by inflation, but $\Lambda$ varies on scales much larger than the present Hubble horizon. Then galaxies are formed only in small $\Lambda$ regions, and the cosmological constant problem is solved by the anthropic argument. Because of the increased degrees of freedom in metric dynamics, the theory predicts new non-oscillatory modes of metric anisotropy generated by quantum fluctuation during inflation, and CMB B-mode polarization would be observed differently from the standard predictions by general relativity.

Statefinder diagnostic for a generalized Proca model

In this paper, we apply the statefinder diagnostic on the cosmology in the framework of the generalized Proca theories with derivative self-interactions possessing three propagating physical degrees of freedom. We discuss the evolving trajectories of the statefinder parameters with the parameter n of this model recently fitted as n = 0.254 and n = 0.16 by use of the current observational data and find that some typical characteristic of the evolution of statefinder parameters makes the model distinguishable between n = 0.254 case and n = 0.16 case and also from other dark energy models.

Hamiltonian Analysis of 3-Dimensional Connection Dynamics in Bondi-like Coordinates*

The Hamiltonian analysis for a 3-dimensional connection dynamics of , spanned by {L−+, L−2, L+2} instead of {L01, L02, L12}, is first conducted in a Bondi-like coordinate system. The symmetry of the system is clearly presented. A null coframe with 3 independent variables and 9 connection coefficients are treated as basic configuration variables. All constraints and their consistency conditions, the solutions of Lagrange multipliers as well as the equations of motion are presented. There is no physical degree of freedom in the system. The Bañados–Teitelboim–Zanelli (BTZ) spacetime is discussed as an example to check the analysis. Unlike the ADM formalism, where only non-degenerate geometries on slices are dealt with and the Ashtekar formalism, where non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well, in the present formalism the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate.

Gravity from the constructive approach standpoint

The general theory of relativity was first formulated as geometrodynamics, i.e., as a theory where the space–time metric is a dynamic quantity. But it is currently obvious that from the standpoint of particle physics, gravity is simply the theory of a massless spin-2 particle. We show that many important properties of gravity itself and of its possible extensions and modifications can be understood starting from the simple physical requirement that the number of physical degrees of freedom is correct and there are no nonphysical degrees of freedom.

General invertible transformation and physical degrees of freedom

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

Polyakov loop in a non-covariant operator formalism

We discuss a Polyakov loop in non-covariant operator formalism which consists of only physical degrees of freedom at finite temperature. It is pointed out that although the Polyakov loop is expressed by a Euclidean time component of gauge fields in a covariant path integral formalism, there is no direct counterpart of the Polyakov loop operator in the operator formalism because the Euclidean time component of gauge fields is not a physical degree of freedom. We show that by starting with an operator which is constructed in terms of only physical operators in the non-covariant operator formalism, the vacuum expectation value of the operator calculated by trace formula can be rewritten into a familiar form of an expectation value of Polyakov loop in a covariant path integral formalism at finite temperature for the cases of axial and Coulomb gauge.

Features of the three-phonon acousto-optical interaction due to elastic waves of finite amplitude and an advanced spectrum analysis of optical signals

The unexpected features of square-law nonlinearity inherent in the noncollinear three-phonon acousto-optical interaction controlled by elastic waves of finite amplitude in birefringent crystals with linear acoustic attenuation are distinguished and investigated. They lead to breakthrough applications of strongly nonlinear three-phonon interaction to linear optical spectrum analysis with ∼100% efficiency and qualitatively improved resolution. A principally new physical degree of freedom, unique for this nonlinear phenomenon, is revealed and characterized. The indispensable theoretical developments and proof-of-principle acousto-optical experiments with specially designed wide-aperture tellurium dioxide cells are presented. The obtained experimental results confirm the elaborated approaches, promising potentially the highest possible spectral resolution that one can expect in principle from the acousto-optical technique within optical spectrum analysis.

Comments on interactions in the SUSY models

We consider special supersymmetry (SUSY) transformations with $m$ generators $\overleftarrow{s}_{\alpha }$ for a certain class of models and study some physical consequences of Grassmann-odd transformations which form an Abelian supergroup with finite parameters and respective group-like elements being functionals of field variables. The SUSY-invariant path integral measure within conventional quantization implies the appearance, under a change of variables related to such SUSY transformations, of a Jacobian which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of ${N}=1$ and $N=2$ supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with $(1,1)$ physical degrees of freedom. It is shown that the interaction terms $U_{tr}$ have a corresponding SUSY-exact form: $U_{tr}=% \big(V_{(1)}\overleftarrow{s};V_{(2)}\overleftarrow{\bar{s}}\overleftarrow{s}% \big)$ naturally generated in this generalized formulation. We argue that the case of non-trivial interactions cannot be obtained in such a way.

Note about a pure spin-connection formulation of general relativity and spin-2 duality in (A)dS

We investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual gauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation as a massive graviton in the flat spacetime of the same dimension. We give a detailed proof that the physical degrees of freedom indeed correspond to a massless graviton propagating around the (anti-) de Sitter background and finally speculate about a possible nonlinear pure-connection theory dual to General Relativity with cosmological constant.

Scalar perturbation potentials in a homogeneous and isotropic Weitzenböck geometry

We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory, perturbations are the result of small fluctuations in the tetrad field. The tetrad transforms as a vector in both its holonomic and anholonomic indices. As a result, in the gauge invariant formalism, physical degrees of freedom are those combinations of perturbation parameters which remain invariant under a diffeomorphism in the coordinate frame, followed by an arbitrary rotation of the local inertial (Lorentz) frame. We derive these gauge invariant perturbation potentials for scalar perturbations and present the gauge invariant field equations governing their evolution.

BMS in cosmology

Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.

Linearized gravity with matter time

We study general relativity with pressureless dust in the canonical formulation, with the dust field chosen as a matter time gauge. The resulting theory has three physical degrees of freedom in the metric field. The linearized canonical theory reveals two graviton modes and a scalar mode. We find that the graviton modes remain Lorentz covariant despite the time gauge, and that the scalar mode is ultralocal. We also discuss a modification of the theory to include a parameter in the Hamiltonian that is analogous to that in Horava–Lifshitz models. In this case the scalar mode is no longer ultralocal and it acquires a propagation speed that is dependent on the deformation parameter.

Gravitational scalar–tensor theory

We consider a new form of gravity theories in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is ghost-free under an appropriate choice of the functional form of the Lagrangian. This model possesses 2 + 2 physical degrees of freedom, namely 2 scalar degrees and 2 tensor degrees. We exhaust all such theories with the Lagrangian of the form , where R is the Ricci scalar, and then we show some examples beyond this ansatz. In the course of the analysis, we prove the equivalence between these examples and a subclass of generalized bi-Galileon theories.