In this note, we examine the scattering of two identical fermions in theories where fermionic fields minimally coupled to higher derivative gravity. In particular, we consider the extension of general relativity with $R^2$ corrections or non-local terms. We expand the action of fermions around the flat space background and obtain two fermion-one graviton vertex. Then, by considering the scattering amplitude of two fermions, we calculate the non-relativistic limit and that obtain the potential for two fermion-fermion interaction which would be the usual Newtonian potential corrected with a Yukawa-like term. At the end, we briefly discuss the astronomical effects of such Yukawa-like potential by computing the gravitational pressure of a spherical star and use it for a white dwarf to obtain quantum corrections of Chandrasekhar radius.
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.
Working with a magnetic field periodic along $Oz$ and decaying in time, we deal with the Dirac-type equation characterizing the fermions evolving in magnetar's crust. For ultra-relativistic particles, one can employ the perturbative approach, to compute the conserved current density components. If the magnetic field is frozen and the magnetar is treated as a stationary object, the fermion's wave function is expressed in terms of the Heun's Confluent functions. Finally, we are extending some previous investigations on the linearly independent fermionic modes solutions to the Mathieu's equation …
A model is proposed, according to which the metric tensor field in the standard gravitational Lagrangian is decomposed into a projection (generally - with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary 4-vector field and a tensor part along the same vector field. A theorem has been used, according to which the variation and the partial derivative, when applied to a tensor field, commute with each other if and only if the tensor field and its variation have zero covariant derivatives, provided also the connection variation is zero. Since the projection field obviously…
We discuss the consequences of higher derivative Lagrangians of the form $α_1 A_μ(x)\dot{x}^μ$, $α_2 G_μ(x)\ddot{x}^μ$, $α_3 B_μ(x)\dddot{x}^μ$, $α_4 K_μ(x)\ddddot{x}^μ$, $\cdots$, $U_{(n)μ}(x)x^{(n)μ}$ in relativistic theory. After establishing the equations of the motion of particles in these fields, we introduce the concept of the generalized induction principle assuming the coupling between the higher fields $U_{(n),μ}(x),\ n\geq1$ with the higher currents $j^{(n)μ}=ρ(x)x^{(n)μ}$, where $ρ(x)$ is the spatial density of mass or of electric charge. In addition, we discuss the analogy of the …
We discuss some aspects of the gravitational interaction of the relativistic quantum particles with spin 1/2. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. The quasi-relativistic limit of the theory is then analyzed. Using the analogous method, we obtain the exact Cini-Touschek transformation and discuss the ultra-relativistic limit of the fermion theory. We show that the Foldy-Wouthuysen transformation is not uniquely defined, and the corresponding ambiguity is deeply rooted in the relativistic quantum theory.
Stress-energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld-van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress-energy. The differences in th…
The main concepts of general relativistic thermodynamics and general relativistic statistical mechanics are reviewed. The main building block of the proper relativistic extension of the classical thermodynamics laws is the four-temperature vector β, which plays a major role in the quantum framework and defines a very convenient hydrodynamic frame. The general relativistic thermodynamic equilibrium condition demands βto be a Killing vector field. We show that a remarkable consequence is that all Lie derivatives of all physical observables along the four-temperature flow must then vanish.
In order to localize fermions on branes with codimension one, one usually introduces the Yukawa coupling between fermions and background scalar fields or the recently proposed derivative fermion-scalar coupling in [Phys. Rev. D 89 (2014) 086001]. In this paper, we explore the coupling between a spinor field $Ψ$ and the scalar curvature of spacetime $R$, $ηΨΓ^M\partial_M F(R)γ^5\barΨ$ with $F(R)$ a function of $R$, to investigate localization of the fermion. Because of $Z_2$ symmetry of the extra dimension, the new coupling mechanism proposed here can easily deal with the problem encountered in…
Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear sp…
We discuss a covariant extension of interactions between scalar fields and fermions in a flat space-time. We show, in a covariant theory, how to evade fermionic ghosts appearing because of the extra degrees of freedom behind a fermionic nature even in the Lagrangian with first derivatives. We will give a concrete example of a quadratic theory with up to the first derivative of multiple scalar fields and a Weyl fermion. We examine not only the maximally degenerate condition, which makes the number of degrees of freedom correct, but also a supplementary condition guaranteeing that the time evolu…
It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmolo…
We analyse the non-relativistic approximation of the Dirac equation for slow fermions moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential, induced by a static metric of spacetime. The derivation of the non-relativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy-Wouthuysen (SFW) transformation. We discuss the chameleon field as source of a torsion field and torsion-matter interactions.
Superfluids under an intense gravitational field are typically found in compact stellar cores. Most treatments of these superfluids, however, are done using a flat spacetime background. In this paper, the effect of spacetime curvature on relativistic superfluids is investigated. The scalar-field superfluid in a background metric of a typical star core is considered first. It is found that the superfluid formed inside a compact object can not be of spherical shape. Explicit numerical calculation of the gravitational correction to the superfluid order parameter is performed for two specific exam…
In view of growing interest in long range scalar forces in the early universe to generate primordial black holes, we study in detail the general relativistic formulation of a Fermi gas interacting with a scalar field in cosmology. Our main finding is that the Yukawa interaction leads to a solution where the scalar field oscillates around zero fermion mass and all energy densities decay as radiation. On one hand, we show that if the Fermi gas starts relativistic, it could stay relativistic. On the other hand, if the fermions are initially non-relativistic, they remain non-relativistic for all p…
In this letter, we systematically explore the holographic (non-)relativistic fermionic spectrum without/with dipole coupling dual to Born-Infeld anti-de Sitter (BI-AdS) black hole. For the relativistic fermionic fixed point, this holographic fermionic system exhibits non-Fermi liquid behavior. Also, with the increase of BI parameter $γ$, the non-Fermi liquid becomes even "more non-Fermi". When the dipole coupling term is included, we find that the BI term makes it a lot tougher to form the gap. While for the non-relativistic fermionic system with large dipole coupling in BI-AdS background, wit…
This letter is dedicated to providing proof of two statements concerning the gradient expansion of relativistic hydrodynamics. The first statement is that \textit{the ordering of transverse derivatives is irrelevant in the gradient expansion of a non-conformal fluid}. The second statement is that \textit{the longitudinal projection of the Weyl covariant derivative can be eliminated in the gradient expansion of a conformal fluid}. This second statement does not apply to curvature tensors. In the conformal case, we know that the ordering of Weyl covariant derivatives is irrelevant in the gradien…
We show that some higher derivative theories have a BRST symmetry. This symmetry is due to the higher derivative structure and is not associated to any gauge invariance. If physical states are defined as those in the BRST cohomology then the only physical state is the vacuum. All negative norm states, characteristic of higher derivative theories, are removed from the physical sector. As a consequence, unitarity is recovered but the S-matrix is trivial. We show that a class of higher derivative quantum gravity theories have this BRST symmetry so that they are consistent as quantum field theorie…
We find the entire form of the amplitude of two fermion strings (with different chirality), a massless scalar field and one closed string Ramond-Ramond (RR) in IIA superstring theory which is different from its IIB one. We make use of a very particular gauge fixing and explore several new couplings in IIA. All infinite $u$- channel scalar poles and $t,s$- channel fermion poles are also constructed. We find new form of higher derivative corrections to two fermion two scalar couplings and show that the first simple $(s+t+u)-$ channel scalar pole for $p+2=n$ case can be obtained by having new hig…
Inspired by the recently discovered non-relativistic fermionic fixed points, we investigate how the presence of bulk dipole coupling modifies the spectral function at one of these novel fixed points. As a result, although the infinite flat band is always visible in the presence of the bulk dipole coupling as well as chemical potential, the band is modified in a remarkable way at small momenta up to the order of magnitude of bulk dipole coupling. On the other hand, like a phoenix, a new Fermi surface sprouts from the formed gap when the bulk dipole coupling is pushed up further such as to overs…
We analyse a non-relativistic approximation of the Dirac equation for slow fermions, coupled to the chameleon field and torsion in the spacetime with the Schwarzschild metric, taken in the weak gravitational field of the Earth approximation. We follow the analysis of the Dirac equation in the curved spacetime with torsion, proposed by Kostelecky (Phys. Rev. D69, 105009 (2004)), and apply the Foldy--Wouthuysen transformations. We derive the effective low-energy gravitational potentials for slow fermions, coupled to the gravitational field of the Earth, the chameleon field and to torsion with mi…
By dealing with the evaluation of string theory correlators of $<V_C V_T V_{\barΨ} V_Ψ>$, the complete and closed form of the amplitude of two fermion fields, one tachyon and one closed string Ramond-Ramond field in type IIB superstring theory is found. Specifically by comparing infinite tachyon poles in field theory amplitude with infinite tachyon poles of the S-matrix of string amplitude (for $p+1=n$ case), all the infinite higher derivative corrections of two tachyons and two fermions (in type IIB) to all orders of $α'$ have been discovered. Using these new couplings, we are able to produce…
We study relativistic star solutions in second-order generalized Proca theories characterized by a $U(1)$-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central d…
Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fiertz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4-derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac …
