We construct the canonical constitutive relations for a fluid description of a system with a spin current, valid in an arbitrary number of dimensions in the absence of parity breaking or time reversal breaking terms. Our study encompasses the hydrostatic partition function, the entropy current, Kubo formula, conformal invariance, and the effect of charge. At some stages of the computation we turn on a background torsion tensor which naturally couples to the spin current.
We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial and torsion fields. The consistent hydrodynamical formulation is constructed for the many-particle quantum system of Dirac fermions on the basis of the nonrelativistic Pauli-like equation obtained via the Foldy-Wouthuysen transformation. With the help of the Madelung decomposition approach, the explicit relations between the microscopic and macroscopic fluid variables are derived. The closed system of equations of quantum hydrodynamics enc…
Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport …
In this paper we consider the most general field equations for a system of two fermions of which one single-handed, showing that the spin-torsion interactions among these spinors have a structure identical to that of the electroweak forces among leptons; possible extensions are discussed.
In a previous paper we considered the most general field equations for a system of two fermions of which one single-handed, showing that the spin-torsion interactions among these spinors had the same structure of the electroweak forces among leptons; in this paper we consider the most general field equations for a system of two fermions, showing that the spin-torsion interactions among these spinors have a structure similar to that of the electroweak forces among hadrons: possible differences are discussed, and consequently further extensions are speculated.
In this paper we show how in the most natural extension of gravity with torsion, fermion fields are endowed with running coupling in spinorial interaction, that are shown to reproduce the strength and structure of the leptonic weak forces.
The WZNW and string models are considered in the terms of the initial and invariant chiral currents assuming that the internal and external torsions coincide (anticoincide) and they are the structure constants of the $SU(n),SO(n),$ $SP(n)$ Lie algebras. These models are the auxiliary problems in order to construct integrable equations of hydrodynamic type. It was shown that the WZNW and string models in terms of invariant chiral currents are integrable for the constant torsion associated with the structure constants of the $SU(2),$ $SO(3),$ $SP(2)$ and $SU(3)$ algebras only. The equation of mo…
It is shown that the interactions between the fermion and the gravitational fields are due to the torsion field. The torsion field is considered to be a potential one, like the electromagnetic and gravitational fields. The field equations are obtained, which describe the interactions of the torsion field with the conventional physical fields. The general covariant Lagrangian of the gravitational field, based on the torsion field, is derived. Experiment is proposed to test the theory.
Torsion propagation and torsion-spin coupling are studied in the perspective of the Velo-Zwanziger method of analysis; specifically, we write the most extensive dynamics of the torsion tensor and the most exhaustive coupling that is permitted between torsion and spinors, and check the compatibility with constraints and hyperbolicity and causality of field equations: we find that some components of torsion and many terms of the torsion-spin interaction will be restricted away and as a consequence we will present the most general theory that is compatible with all restrictions.
We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.
We extend the null background construction of [arXiv:1505.05677,arXiv:1509.04718] to include torsion and a conserved spin current, and use it to study gauge and gravitational anomalies in Galilean theories coupled to torsional Newton-Cartan backgrounds. We establish that the relativistic anomaly inflow mechanism with an appropriately modified anomaly polynomial, can be used to generate these anomalies. Similar to relativistic case, we find that Galilean anomalies also survive only in even dimensions. Further, these anomalies only effect the gauge and rotational symmetries of a Galilean theory;…
We investigate the relationship between Hall viscosity, spin density and response to geometric torsion. For the most general effective action for relativistic gapped systems, the presence of non-universal terms implies that there is no relationship between torsion response and Hall viscosity. We also consider free relativistic and non-relativistic microscopic actions and again verify the existence of analogous non-universal couplings. Explicit examples demonstrate that torsion response is unrelated to both Hall viscosity and spin density. We also argue that relativistic gapped theories must ha…
Starting from an action that describes a Dirac fermion, we propose and analyze a model based on a low-relativistic Pauli equation coupled to a torsion-like term to study Spin Hall Effect (SHE). We point out a very particular connection between the modified Pauli equation and the (SHE), where what we refer to torsion as field playing an important rôle in the spin-orbit coupling process. In this scenario, we present a proposal of a spin-type current, considering the tiny contributions of torsion in connection with geometrical properties of the material.
A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy-momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metr…
We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature in terms of the fundamental 4-form. We present an explicit formula for the Riemannian covariant derivative of the fundamental 4-form in terms of its exterior differential. We show the vanishing of the (\hat)-A genus and obtain a linear relation between Betti numbers of a compact Spin(7) manifolds which are locally but not globally conformally equivalent to a …
On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein-Cartan gravity interacting with classical spinor field is proposed. In this approach the spinor field becomes an auxiliary field and the dynamical equation for this field (the Heisenberg equation) is a dynamical, gravitational equation for torsion. The simplest version of this theory is examined where the metric degrees of freedom are frozen and only torsion plays a role. A spherically symmetric solution of this theory is examined. This solution can be interpreted, in the spirit …
Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks.
Relativistic gravitational anomalies lead to anomalous transport coefficients that can be activated at finite temperature in condensed matter systems with gapless fermions. The chiral vortical effect (CVE) is an anomalous chiral current along a rotation axis, expressed in terms of a gravimagnetic field and a gravitational anomaly. Another one, the chiral torsional effect (CTE), arises from hydrodynamically independent frame fields and connection. We discuss the relation of CVE, CTE and gravitational anomalies for relativistic fermions from the perspective of torsion and the Nieh-Yan anomaly. T…
We show that it is possible to formulate the classical Einstein-Maxwell-Dirac theory of spinors interacting with the gravitational and electromagnetic fields as the Einstein-Cartan-Kibble-Sciama theory with the Ricci scalar of the traceless torsion, describing gravity, and the torsion trace acting as the electromagnetic potential.
Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we study the dynamics of magnetization and how it is affected by the presence of torsion. We consider that torsion interacting terms in Dirac equation appear in two ways one of these is thhrough the covariant derivative considering the spin connection and gauge magnetic field and the other is through a non-minimal spin torsion coupling. We show within this framework, that it is possible to obtain the most general Landau, Lifshitz and Gilbert (LLG) equation including the torsion effects, where we refe…
A notion of distorted torsion tensor was introduced by Okubo, in the establishment of the Nijenhuis-Bianchi identity and of BRST-like operators. These quantities are constructed with the help of the Nijenhuis tensor, which in turn is defined in terms of a (1,1) tensor $S^λ_μ$. This tensor enters the construction of the distorted torsion tensor. We use this tensor to extend the teleparallel equivalent of general relativity (TEGR) into a theory defined by the tetrad fields and by the tensor $S^λ_μ$. The ordinary TEGR is recovered if $S^λ_μ=δ^λ_μ$. We consider the flat space-time formulation of t…
We show that the intrinsic angular momentum of matter in curved spacetime requires the metric-affine formulation of gravity, in which the antisymmetric part of the affine connection (the torsion tensor) is not constrained to be zero but is a variable in the principle of stationary action. Regarding the tetrad and spin connection (or the metric and torsion tensors) as independent variables gives the correct generalization of the conservation law for the total (orbital plus intrinsic) angular momentum to the presence of the gravitational field. The metric-affine formulation extends general relat…
We report the first experimental upper bound to our knowledge on possible in-matter torsion interactions of the neutron from a recent search for parity violation in neutron spin rotation in liquid He-4. Our experiment constrains a coefficient $ζ$ consisting of a linear combination of parameters involving the time components of the torsion fields $T^μ$ and $A^μ$ from the nucleons and electrons in helium which violates parity. We report an upper bound of $|ζ|<9.1x10^{-23}$ GeV at 68% confidence level and indicate other physical processes that could be analyzed to constrain in-matter torsion.
We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltoni…
We considered two types of string models: on the Riemmann space of string coordinates with null torsion and on the Riemman-Cartan space of string coordinates with constant torsion. We used the hydrodynamic approach of Dubrovin, Novikov to integrable systems and Dubrovin solutions of WDVV associativity equation to construct new integrable string equations of hydrodynamic type on the torsionless Riemmann space of chiral currents in first case. We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydr…
We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydrodynamic type on the Riemmann space of the chiral primitive invariant currents and on the chiral non-primitive Casimir operators as Hamiltonians.
One of the greatest unsolved issues of the physics of this century is to find a quantum field theory of gravity. According to a vast amount of literature unification of quantum field theory and gravitation requires a gauge theory of gravity which includes torsion and an associated spin field. Various models including either massive or massless torsion fields have been suggested. We present arguments for a massive torsion field, where the probable rest mass of the corresponding spin three gauge boson is the Planck mass.
In most theories of gravity involving torsion, the source for torsion is the intrinsic spin of matter. Since the spins of fermions are normally randomly oriented in macroscopic bodies, the torsion generated is normally negligible. However, in a recent paper, Mao et al. point out that there is a class of theories in which the angular momentum of macroscopic spinning bodies generates a significant amount of torsion. They argue that by the principle of action equals reaction, one would expect the angular momentum of test bodies to couple to a background torsion field, and therefore the precession…
The interaction of the light with propagating axial torsion fields in the presence of an external magnetic field has been investigated. Axial torsion fields appearing in higher derivative quantum gravity possess two states, with spin one and zero, with different masses. The torsion field with spin-0 state is a ghost that can be removed if its mass is infinite. We investigate the possibility when the light mixes with the torsion fields resulting in the effect of vacuum birefringence and dichroism. The expressions for ellipticity and the rotation of light polarization axis depending on the coupl…
