Quadratic Lagrangians and massive gravitons

An expansion of a quadratic Lagrangian in a series in small corrections to a flat metric yields the Lagrangian of the free gravitational field (first term of the expansion); by a substitution of the field variables this is reduced to a sum of standard Lagrangians that define massless and massive scalar and tensor fields. Independent variation of the corresponding Lagrangian with respect to the massive scalar and tensor gravitational fields is possible only if the coupling constants in the quadratic Langrangian satisfy a certain relation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 15–20, June, 1975.I thank Professor D. D. Ivanenko for his constant interest.     

Gravity as the square of Yang‐Mills: implications for 𝒩 = 8 supergravity

The pure gravity Lagrangian can be written as the “square” of the pure Yang‐Mills Lagrangian to second order in coupling constants. This paper uses this form of the gravity Lagrangian as a starting point to arrive at a compact light‐cone superspace Lagrangian for 𝒩 = 8 supergravity to order κ².     

Taming of divergences in a unitary model of massive fermions, vectors and scalars

We consider a massive vector field, interacting through three-field interactions with a massive scalar and spinor field, in a unitary model. There are divergences that cannot be removed by introduction of counter terms into the Lagrangian. It is shown that it is possible to tame many of them and to remove the remaining divergences by appropriate choices of the coupling constants.     

Scaling behavior of semiclassical gravity

Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.     

Nonlinear Resonant Interaction of Two Longitudinal Waves and a Transverse Wave in a Hot Magnetized Plasma

By Whitham's method of averaged Lagrangian and using Low's form of Lagrangian, coupled mode equations and coupling coefficients are derived for resonant nonlinear interaction of two longitudinal and one transverse wave in a magnetized plasma, in which the later wave propagates along the external uniform magnetic field. The limiting form of these coupling coefficients are obtained when the external magnetic field vanishes.     

Restrictions on the interaction between massive vector mesons

A critical investigation of the most general Lagrangian describing any number of massive vector mesons coupled through parity conserving interactions with dimensionless coupling constants is made. The theory is required to satisfy the following three conditions which are necessary on physical grounds: the presence of the interaction must not change the number of degrees of freedom of the system, the equations must describe propagation, and the propagation must take place at a speed less than that of light. One finds that some of the coupling constants are zero and others are related. The Lagrangian density takes a very simple form which generalizes, apart from the mass term, the Yang-Mills Lagrangians.     

A Modified Theory of Gravity with Torsion and Its Applications to Cosmology and Particle Physics

In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German Eigenspinoren des LadungsKonjugationsOperators designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field’s self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.     

Isovector Scalar Field Effects in Asymmetric Nuclear Matter

Density-dependent parametrization models of the nucleon-meson coupfing constants, including the isovector scalar δ-field, are applied to asymmetric nuclear matter. The nuclear equation of state （EOS） and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field （RMF） hadron theory. It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the （~-field effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence of the interactions.     

A note on inequalities for the masses of the lightest ππ resonances in multicoloured QCD

We derive and analyse inequalities relating masses of the lightest ππ resonances (ρ and σ) to coupling constants of the effective chiral Lagrangian in the limit of a large number of colours. Received: 15 July 2001 / Accepted: 23 October 2001     

Some remarks on the baryon-meson couplings in the 1/N_c expansion

The original results for the baryon-pion couplings in the large QCD can be understood in a simpler way in the Hartree-Fock picture. The large relation and its correction between the heavy baryon-meson coupling and the light baryon-meson coupling are emphasized. Application to the baryon- meson interactions is straightforward. The implications of recent experimental result for the strong coupling constants of the heavy baryon chiral Lagrangian are discussed. Received: 31 March 1997 / Published online: 20 February 1998     

Non-minimally coupled quintom model inspired by string theory

In this Letter we consider a quintom model of dark energy with a single scalar field T given by a Lagrangian which inspired by tachyonic Lagrangian in string theory. We consider non-minimal coupling of tachyon field to the scalar curvature, then we obtain the equation of state (EoS), and the condition required for the model parameters when ω crosses over −1.     

Extracting information on renormalized coupling constants of contact interactions of the chiral perturbation theory lagrangian from the phase-shift analysis of π<Emphasis Type="Italic">N</Emphasis> scattering

The analytic approach to the construction of the effective theory of strong interactions in the low-energy range is developed and its application to pion-nucleon scattering is considered. A model-independent definition of renormalized coupling constants of contact interactions of the effective chiral perturbation theory Lagrangian is proposed. With the help of the available data of pion-nucleon phase-shift analysis the information on these constants is extracted.     

Large N_ c in chiral perturbation theory

The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan–Manohar transformation is in conflict with these rules and is suppressed to all orders in . The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess–Zumino–Witten term, which accounts for the U(3)U(3) anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in , but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance. Received: 14 July 2000 / Published online: 27 October 2000     

On energy-momentum tensors as sourcesof spin-2 fields

The improvement terms in the generalised energy-momentum tensor of Callan, Coleman and Jackiw can be derived from a variational principle if the Lagrangian is generalised to describe coupling between ‘matter’ fields and a spin-2 boson field. The required Lorentz-invariant theory is a linearised version of Kibble-Sciama theory with an additional (generally-covariant) coupling term in the Lagrangian. The improved energy-momentum tensor appears as the source of the spin-2 field, if terms of second order in the coupling constant are neglected.     

Minimal coupling in spin-2 field

It is shown that the spin-2 Lagrangian of Watanabe and Bhargava can be generalised by the introduction of a real parameter b associated with derivative ordering. After minimal coupling the spin-2 dynamical equations of Nath and Velo and Zwanziger can be derived as special cases. The constraint situation in these equations is then summarised and related to the first-order Lagrangian approach of Federbush, Chang, et al. Only one value of the parameter b gives a correct manifold of states after coupling. Finally it is shown that the auxiliary field approach to spin-2 proposed by Chang is dynamically inconsistent under minimal coupling.     

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.     

Dual field theory of strong interactions

A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac chargeg=(137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector bosonW ^±. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant=1/137.     

Electroweak Chiral Lagrangian for Neutral Higgs Boson

A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.     

Ambiguities Appearing in the Study of Time-Dependent Constants of Motion for the One-Dimensional Harmonic Oscillator

A family of time-dependent constants of motionfor the one-dimensional harmonic oscillator is derived.The relation between constants of motion, Lagrangian,and Hamiltonian is described. A well-defined time-dependent Lagrangian (for whichEuler–Lagrange equations and Legendretransformation are fully satisfied) is not uniquelydetermined.