On the structure of all the equations for spin 3/2 without auxiliary spin 3/2; their vector-spinor form

1984 ◽  
Vol 80 (4) ◽  
pp. 429-440
Author(s):  
G. Labonté
Keyword(s):  
Spinor Form

scholarly journals Intertwining differential operators for spinor-form representations of the conformal group

1984 ◽  
Vol 54 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Thomas P. Branson
Keyword(s):  
Differential Operators ◽  
Conformal Group ◽  
Spinor Form

Relativistic kinematics of a classical point particle in spinor form

1957 ◽  
Vol 5 (4) ◽  
pp. 784-809 ◽  
Author(s):  
F. Gürsey
Keyword(s):  
Point Particle ◽  
Relativistic Kinematics ◽  
Spinor Form ◽  
Classical Point

scholarly journals SPIN-$\frac{3}{2}$ POTENTIALS IN BACKGROUNDS WITH BOUNDARY

1995 ◽  
Vol 04 (06) ◽  
pp. 735-747 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
GABRIELE GIONTI ◽  
ALEXANDER YU. KAMENSHCHIK ◽  
IGOR V. MISHAKOV ◽  
GIUSEPPE POLLIFRONE
Keyword(s):  
Boundary Conditions ◽  
Field Equations ◽  
Gauge Freedom ◽  
Massless Case ◽  
Gauge Transformations ◽  
Local Boundary ◽  
Ricci Flat ◽  
Spinor Form

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat. The analysis of other gauge transformations confirms that, in the massless case, the only admissible class of Riemannian backgrounds with boundary is totally flat.

COMPLEXIFIED THEORY OF POSITIVE-FREQUENCY MAXWELL-DIRAC FIELDS

1993 ◽  
Vol 08 (21) ◽  
pp. 3697-3719 ◽  
Author(s):  
J.G. CARDOSO
Keyword(s):  
Wave Equations ◽  
Lagrangian Density ◽  
Variational Principles ◽  
Equations Of Motion ◽  
Dirac Equations ◽  
Spinor Form ◽  
Equivalent Wave ◽  
Symmetric Operators ◽  
Positive Frequency ◽  
Component Spinor

We present a method whereby the equations of motion yielding the explicit two-component spinor form of the complete Maxwell-Dirac theory in complex Minkowski space may be directly derived from two variational principles. One of these dynamical statements gives rise to the first half of the electromagnetic theory which particularly appears as the equations of motion involving a slightly modified version of the free part of the conventional Maxwell Lagrangian density. The other principle actually involves a holomorphic two-spinor expression for the full Maxwell-Dirac Lagrangian density which leads to the second half along with the Dirac equations that carry the relevant covariant derivative operator. It is shown explicitly how the Bianchi identities of the complete theory can be established in a manifestly covariant way. A system of essentially equivalent wave equations for positive-frequency photons and electrons is then exhibited. In particular, we make use of certain skew-symmetric operators to obtain an extended form of the Feynman-Gell-Mann equations.

SPINORS IN THE DYNAMICAL THEORY OF SPINNING PARTICLES

1952 ◽  
Vol 30 (3) ◽  
pp. 226-234 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Hamiltonian Dynamics ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Total Spin ◽  
System Of Equations ◽  
Poisson Brackets ◽  
Spin Angular Momentum ◽  
Canonical Variables ◽  
Spinor Form ◽  
Set Up

The correspondence between self-dual six-vectors and symmetric spinors of the second rank is used to put into spinor form the rotational equations of motion of a particle analogous to a pure gyroscope or to a symmetrical top. These equations are then split up into an equivalent system of equations in terms of spinors of the first rank. The Lagrangian of each system is set up, and the canonically conjugate variables obtained from it in terms of covariant spinors. But the canonical variables, being not all independent, lead to weak equations in the sense of Dirac. Therefore, Dirac's generalized Hamiltonian dynamics is used in the canonical formulation in terms of Poisson Brackets. The detailed discussion of the symmetrical top case shows that, though the fundamental Poisson Brackets for the total spin angular momentum and the "spin" are the usual ones, those Poisson Brackets-involving the derivative of the "spin" are not unique.

Spinor form of electromagnetism in nonhomogeneous media

1991 ◽  
Vol 29 (9) ◽  
pp. 1157-1165 ◽  
Author(s):  
Pierre Hillion
Keyword(s):  
Nonhomogeneous Media ◽  
Spinor Form

scholarly journals ON THE EQUIVALENCE OF THE MASSLESS DKP EQUATION AND THE MAXWELL EQUATIONS IN THE SHUWER

2005 ◽  
Vol 20 (06) ◽  
pp. 451-465 ◽  
Author(s):  
MUSTAFA SALTI ◽  
ALI HAVARE
Keyword(s):  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Relativistic Wave Equation ◽  
Order Form ◽  
Electric And Magnetic Fields ◽  
Spinor Form ◽  
Strength Tensor ◽  
General Relativistic

In this paper, a general relativistic wave equation is written to deal with electromagnetic waves in the background of the Shuwer. We obtain the exact form of this equation in a second-order form. On the other hand, by using spinor form of the Maxwell equations the propagation problem is reduced to the solution of the second-order differential equation of complex combination of the electric and magnetic fields. For these two different approaches, we obtain the spinors in terms of field strength tensor. We show that the Maxwell equations are equivalence to the mDKP equation in the Shuwer.

scholarly journals A Spinor Model for Cascading Two-port Scattering Matrices In Conformal Geometric Algebra

2021 ◽  
Author(s):  
Alexander Arsenovic
Keyword(s):  
Minkowski Space ◽  
Network Theory ◽  
Geometric Algebra ◽  
Scattering Matrix ◽  
Conformal Geometric Algebra ◽  
Dimensional Minkowski Space ◽  
Scattering Matrices ◽  
Spinor Form ◽  
Spinor Model

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port scattering matrix as a rotation in four dimensional Minkowski space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional microwave network theory. Techniques to translate two-port scattering matrix in and out of spinor form are given. Once the translation is laid out, geometric interpretations are given to the physical properties of reciprocity, loss, and symmetry and some mathe- matical groups are identified. Methods to decompose a network into various sub-networks, are given. An example application of interpolating a 2-port network is provided demonstrating an advantage of the spinor model. Since rotations in four dimensional Minkowski space are Lorentz transformations, this model opens up the field of network theory to physicists familiar with relativity, and vice versa.

scholarly journals TWISTORS IN CONFORMALLY FLAT EINSTEIN FOUR-MANIFOLDS

1996 ◽  
Vol 05 (05) ◽  
pp. 481-493
Author(s):  
GIAMPIERO ESPOSITO ◽  
GIUSEPPE POLLIFRONE
Keyword(s):  
Integrability Condition ◽  
Conformally Flat ◽  
Derivative Operator ◽  
Spinor Fields ◽  
Massive Spin ◽  
Two Component ◽  
Spinor Form ◽  
Four Manifolds ◽  
Partial Connection ◽  
Component Spinor

This paper studies the two-component spinor form of massive spin-[Formula: see text] potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a nonvanishing cosmological constant makes it necessary to introduce a supercovariant derivative operator. The analysis of supergauge transformations of primary and secondary potentials for spin-[Formula: see text] shows that the gauge freedom for massive spin-[Formula: see text] potentials is generated by solutions of the supertwistor equations. The supercovariant form of a partial connection on a nonlinear bundle is then obtained, and the basic equation of massive secondary potentials is shown to be the integrability condition on super β-surfaces of a differential operator on a vector bundle of rank 3. Moreover, in the presence of boundaries, a simple algebraic relation among some spinor fields is found to ensure the gauge invariance of locally supersymmetric boundary conditions relevant for quantum cosmology and supergravity.

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