Left-handed Spin Research Articles

The Holst Action by the Spectral Action Principle

We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.

TORSION INSTEAD OF TECHNICOLOR

We consider the model, which contains a nonminimal coupling of Dirac spinors to torsion. Due to the action for torsion that breaks parity, the left–right asymmetry of the spinors appears. This construction is used in order to provide dynamical electroweak symmetry breaking. Namely, we arrange all Standard Model fermions in the left-handed spinors. The additional technifermions are arranged in right-handed spinors. Due to the interaction with torsion, the technifermions are condensed and, therefore, cause appearance of the gauge boson masses. In order to provide all fermions with masses, we consider two possibilities. The first one is related to an additional coupling of a real massive scalar field to the considered spinors. The second possibility is to introduce the explicit mass term for the mentioned Dirac spinors composed of the Standard Model fermions and the technifermions.

Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions

We show at one-loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories --chiral or otherwise-- defined by means of Seiberg-Witten maps that are the same --barring the gauge group representation-- for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the Standard Model.

The magnetic structure of MnSi under an applied field

Below TC = 29 K the weak itinerant ferromagnet MnSi becomes ordered in a left-handed spin helicalstructure as a result of the Dzyaloshinskii–Moriya (DM) interaction. We give a recipe forcalculating the orientation of the helix under an applied field. The recipe is derived on abasis of a theory recently developed for cubic magnets with DM interaction. The theoryevaluates the ground state energy and the spin wave spectrum. It is shown that inzero field the orientation of the helix depends solely on the anisotropic exchangeinteraction and cubic anisotropy. Under an applied field the helix possesses twotypes of magnetic susceptibility: one parallel and another perpendicular to theapplied magnetic field. The perpendicular susceptibility is related to the fact thatthe helical structure itself is unstable with respect to the small magnetic fieldH applied perpendicularlyto the wavevector k.The spin wave gap Δ provides the stability of the spin wave spectrum of the helix structure and its presence maybe revealed in the magnetic field behaviour. Our calculations show the essence of thefield-induced transformations of the magnetic structure related to the spin wave gap. Theexperimental data provide the evidence for its existence. On the basis of ourfindings we discuss a possible scenario for the quantum phase transition in MnSi.

The influence of training with heavy rugby balls on selected spin pass variables in youth rugby union players

The purpose of this study was to investigate the influence of training with heavy rugby balls on selected spin pass variables in youth rugby union players. Pre-training, 14 participants performed rapid spin passes (using right and left hands) at a wall-mounted target, from 7-m and 10-m distances. Horizontal (linear) and spin (longitudinal angular) velocities of the passes were recorded using a 25Hz video camera. Participants also performed right- and left-handed spin passes for maximal distance. The participants were then randomly divided into two equal groups, to train twice weekly for eight weeks, using either normal or heavy rugby balls. Each individual performed 50-90 rapid spin passes ranging from 5m to 12m with each hand per session. Following training, participants were reassessed using the same pre-training protocols. Significant changes were found pre-to-post training for both the normal ball, and heavy ball groups, for 7-m right-handed horizontal (linear) velocities (9.80+/-0.45 to 10.27+/-0.82ms(-1), and 9.42+/-1.04 to 10.19+/-1.03ms(-1), respectively; p=0.029), 10-m left-handed spin (longitudinal angular) velocities (5.13+/-1.60 to 6.08+/-1.30revss(-1), and 4.39+/-1.62 to 5.81+/-0.65revss(-1), respectively; p=0.014), right-handed maximal distance passes (19.0+/-3.6 to 20.6+/-4.0m, and 18.6+/-3.4 to 20.7+/-4.3m, respectively; p=0.001) and left-handed maximal distance passes (15.3+/-3.2 to 18.1+/-2.5m, and 15.0+/-3.0 to 17.6+/-3.7m, respectively; p<0.000). No significant changes could be attributed to training exclusively with the heavy rugby balls. The results of this investigation suggest that intense repetitive passing practice increases a small number of selected spin passing variables in youth rugby union players.

The spin chirality in MnSi single crystal probed by small angle scattering with polarized neutrons

The weak itinerant ferromagnet MnSi orders with a left-handed helical spin structure below T C=29 K. The helicity with a vector m=[ S 1 × S 2]/S 2 along the crystallographic axis [1 1 1] is realized by an antisymmetric Dzyaloshinski–Moriya interaction. The small angle diffraction study with polarized neutrons on a single MnSi crystal was performed within the temperature range from 10 K to T C and the magnetic field B from 1 to 350 mT. The single crystal was oriented in such a way that two axes [1 1 1] and [1 1 −1] were set in a plane perpendicular to the incident beam. Four major diffraction peaks at ± q 1 and ± q 2 along the axes and four minor peaks at q=± q 1± q 2 were observed. The intensity I p= I(+ P 0)+ I(− P 0), the polarization P p=[ I(+ P 0)− I(− P 0)]/ I p and the position q p of the peaks were measured as a function of the temperature and the magnetic field. From intensity of the peaks the chiral critical exponent is obtained as β=0.47±0.04.

VACUUM POLARIZATION OF A CHARGED MASSLESS FERMIONIC FIELD BY A MAGNETIC FLUX IN THE COSMIC STRING SPACETIME

We calculate the vacuum averages of the energy–momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: (i) a homogeneous field inside the tube, (ii) a magnetic field proportional to 1/r, and (iii) a cylindrical shell with δ-function. In these three cases the axis of the infinitely long tubes of radius R coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e. corresponding to the spinor Green's functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy–momentum tensor.

One-loop divergences in anomaly-free non-Abelian axial models

We consider one-loop divergences in a four-dimensional model in which a non-Abelian vector field has an axial vector coupling with a massless left-handed spinor field. This is done by computing the diagonal element of the second Seeley–deWitt coefficient a2(x,x). Even when the coupling is such that the axial anomaly vanishes, divergences arise that are not gauge invariant. Operator regularization is used throughout so as to leave the matrix γ5unambiguously defined. PACS No.: 11.15.q

Massive torsion modes, chiral gravity and the Adler–Bell–Jackiw anomaly

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler–Bell–Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin-½ particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition, it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel–Jacobson–Smolin action of chiral gravity in four dimensions.

Vacuum polarization for a massless spin-1/2 field in the global monopole spacetime at nonzero temperature

In this paper we present the effects produced by temperature in the renormalized vacuum expectation value of the zero–zero component of the energy–momentum tensor associated with a massless left-handed spinor field in the point-like global monopole spacetime. In order to develop this calculation we had to obtain the Euclidean thermal Green function in this background. Because the expression obtained for the thermal energy density cannot be expressed in a closed form, its explicit dependence on temperature is not completely evident. So, in order to obtain concrete information about its thermal behaviour, we develop a numerical analysis of our result in the high-temperature limit for specific values of the parameter α which codify the presence of the monopole.

Vacuum polarization of a massless spinor field in global monopole spacetime

We calculate the renormalized vacuum average of the energy-momentum tensor of massless left-handed spinor field in the pointlike global monopole spacetime using point-separation approach. The general structure of the vacuum average of the energy-momentum tensor is obtained and expressed in terms of $<T^0_0>^{ren}$ component, explicit form of which is analyzed in great details for arbitrary solid angle deficit.

NONLOCALITY AND GRAVITY-INDUCED CP VIOLATION

We consider a space–time dependent relative phase between the right- and left-handed spinors and show that it results in a violation of locality in the presence of gravity once the demand of parity covariance is dropped. This violation of locality is such that it readily interprets itself as a gravity-induced CP violation, and at the same time confirms an earlier remark by Wigner that a representation space carries more information than a wave equation. This happens, as Kirchbach has noted, because while the dimensionality of an irreducible representation space does not depend upon the concrete realization of the symmetry generators, Noether currents (Dirac, versus Majorana, versus the CP violating construct presented here) do. The gravity-induced CP violation provides a dynamical reason on how a neutron star carrying its baryon and lepton numbers can collapse into a black hole and loose information on the latter characteristics.

Invariant regularization of anomaly-free chiral theories

We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for arbitrary representations which satisfy the chiral gauge anomaly and the mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly chiral (Weyl) in that all fields, including the regulators, are left-handed; and only the left-handed spin connection is needed. The scheme is, therefore, well suited for the study of the interaction of matter with all four known forces in a completely chiral fashion. In contrast with the vectorlike formulation, the degeneracy between the Adler-Bell-Jackiw current and the fermion number current in the bare action is preserved by the chiral regularization scheme.

Standard model with gravity couplings

In this paper we examine the coupling of matter fields to gravity within the framework of the standard model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti-)self-dual or left-handed spin connection fields. We review the general framework for introducing the coupling using these fields, and show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C, and T, and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly. \textcopyright{} 1996 The American Physical Society.

Howzat?! Why is there an Over-representation of Left-handed Bowlers in Professional Cricket in the UK?

An analysis of the bowling action of professional cricketers in the UK for four seasons between 1981 and 1991 shows there to be a significant association between handedness and bowling style (seam or spin bowling). Furthermore, there is a significantly higher number of left-handed spin bowlers than would be predicted from the general population, but not left-handed seam bowlers. As the technical differences between left- and right-handed orthodox spin bowlers are much greater than those between left- and right-handed seam bowlers, these data are consistent with the view that the over-representation of left-handed bowlers reported by Wood and Aggleton (1989) is due to strategic rather than neuropsychological factors.

Supersymmetry with no superpartners

A gauge theory of left-handed supergravity and non-supersymmetric left-handed spin- 1 2 matter is obtained from a higher gauge symmetry which is based on a four-dimensional spacetime specified by ( x μ θ α μ ( x)), where θ α μ ( x) is a vector-spinor. The spacetime origin of parity violation is demonstrated.

A lattice approach to spinorial quantum gravity

The authors present a new lattice regularisation of quantum general relativity based on Ashtekar's reformulation (1986) of Hamiltonian general relativity. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. The authors construct lattice versions of these constraints. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

New variables for canonical supergravity

Ashtekar's reformulation (1987) of canonical general relativity is extended to simple supergravity in four dimensions. The key idea is to use the left-handed spin connection as a complex coordinate on the phase space. The constraints are simple polynomial functions of degree four or less when expressed in terms of the new conjugate variables. The reformulation is derived starting from a complex first-order supergravity action. The action is invariant under left- and right-handed supersymmetry transformations which are not conjugate, since the connection varies in the latter case but not in the former.

Nonperturbative quantum geometries

Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field — and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric.

Vertex operator construction of the SO(9,1) Majorana-Weyl spinors in the Neveu-Schwarz-Ramond model

By paying a careful attention to the hermiticity property, the SO(9,1) left-handed Majorana-Weyl spinors are obtained as vertex operators. The hermiticity requires an extra condition on the two-cocycle involved in the vertex operators, whose existence is proved by making an explicit construction.