Relativistic Wave Equations For Particles Research Articles

Solution to the Rarita-Schwinger equations

A systematical method is presented for solving the relativistic wave equations for particles of arbitrary spin. Explicit helicity relativistic wave functions for particles with arbitrary spin are derived rigorously.

Fields on the Poincaré Group: Arbitrary Spin Description and Relativistic Wave Equations

In this paper, starting from a pure group-theoretic point of view, we develop an ap- proach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered as generating functions for conventional spin-tensor fields. The case of two, three, and four dimensions are elaborated in detail. Discrete transformations C; P; T are defined for the scalar fields as automorphisms of the Poincare group. We classify the scalar functions, and ob- tain relativistic wave equations for particles with definite spin and mass. There exist two different types of scalar functions (which describe the same mass and spin), one related to a finite-dimensional nonunitary representation and the other to an infinite- dimensional unitary representation of the Lorentz subgroup. This allows us to derive both usual finite-component wave equations for spin-tensor fields and positive-energy, infinite-component wave equations.

POSSIBILITY OF GEOMETRIC DESCRIPTION OF QUASIPARTICLES IN SOLIDS

New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic crystalline fields is included. The quasiparticles in this space are supposed to be described by the equations structurally similar to the relativistic wave equations for particles in empty space. The generalized Klein–Gordon–Fock equation and the generalized Dirac equation in external electromagnetic field are considered. The applicability of the proposed approach to the case of conduction electron in a crystal is discussed.

Relativistic wave equations for particles in electromagnetic fields

A new type of generalization of the Dirac equation to higher spin particles and antiparticles is given, in case only the terms proportional to the external fields need to be retained.

Acausality of all standard relativistic wave equations with Harish-Chandra degree four

The long-standing conjecture of non-existence of acceptable standard relativistic wave equations for particles of spins s>or=3/2 is proven, for all cases with Harish-Chandra degree four. This is an important step toward the general proof since the only remaining candidate equations have higher HC degrees and therefore are expected to exhibit still worse pathologies.

On the problem of constraints in minimally coupled relativistic wave equations for particles of unique mass

We study the problem of a possible change in the number of constraints in linear relativistic wave equations (-iβ μ ∂ μ +m)ψ=0 for particles of unique mass, on introduction of minimal coupling to an external electromagnetic field. Complementing our earlier work in which we obtained conditions for non-loss of constraints in equations characterised by the minimalβ-algebraβ 0 5 =β 0 3 we derive here the conditions for such theories not to generate more constraints than in the free case. The results are illustrated by considering specific equations and a fallacy in certain conclusions of Kobayashi and Shamaly on this problem is pointed out.

Two-Component Relativistic Wave Equations for Spin-½ Particles

A critical re-examination is made of the derivation from the Kramers equation and the Poincaré covariance of the two-component relativistic wave equations for particles of non-zero mass and spin ½ that have recently been proposed by Biedenharn, Han and van Dam.

Relativistic Wave Equations for Particles with Arbitrary Spin

Relativistic wave equations are derived which generalize the recently obtained Galilei-covariant wave equations for massive particles with any integer or half-integer spin. Imposing a minimality condition on the number of components possessed by the relativistic wave function, it is shown that the index transformation properties of the wave function may be either those of the $(s,0)\ensuremath{\bigoplus}(s\ensuremath{-}\frac{1}{2},\frac{1}{2})$ representation of $\mathrm{SL}(2,C)$ or of the representation $(0,s)\ensuremath{\bigoplus}(\frac{1}{2},s\ensuremath{-}\frac{1}{2})$. The minimal extension of these representations which accommodates reflection symmetry yields the Dirac equation for $s=\frac{1}{2}$, the Duffin-Kemmer equation for $s=1$, and an equation for particles with $s>1$ whose wave-function indices transform according to the $(s,0)\ensuremath{\bigoplus}(s\ensuremath{-}\frac{1}{2},\frac{1}{2})\ensuremath{\bigoplus}(\frac{1}{2},s\ensuremath{-}\frac{1}{2})\ensuremath{\bigoplus}(0,s)$ representation of $\mathrm{SL}(2,C)$. The latter theory possesses $4(2s+1)$ independent components, has no subsidiary conditions, and describes a unique mass, $m\ensuremath{\ne}0$, and a unique spin. The theory admits a simple Lagrangian and Hamiltonian formulation and yields a conserved current. Finally, it is shown that for any spin the equation remains consistent and causal in the presence of a minimally coupled external-electromagnetic-field interaction.

Relativistic Wave Equations for Particles with Internal Structure and Mass Spectrum

Relativistic wave equations may be expected to play two roles, which we will call kinematical and dynamical. In the kinematical sense, a wave equation singles out a particle of definite mass and spin, usually together with its anti-particle counterpart, and specifies how the components of the wave function transform as we change its state of motion or our reference system. This law of transformation must be in accordance with the Poincare group,**) and therefore a wave equation should characterize an irreducible unitary representation of that group appropriate to quantum mechanical description of a particle!) In the dynamical sense, however, a wave equation ought to serve more purposes. It should be able to describe not only an isolated free particle, but also a particle in interaction, at least with classical fields such as the electromagnetic and gravitational fields, and ideally with all other dynamical fields and associated particles. A wave equation then becomes an equation

On the compatibility of relativistic wave equations for particles of higher spin in the presence of a gravitational field

It is known that the equations for particles of spin ⩾ 3/2 become inconsistent when electromagnetic interactions are introduced by the usual rules. An analogous problem is that of the effect of the introduction of gravitational fields on the consistency of the equations. The « natural generalization » of the usual field equations for particles of spin 3/2 is here considered in detail, and it is shown that the equations are compatible if and only if the Riemann space in which the spinor field is contemplated is an Einstein space. This result is discussed.

Relativistic wave equations for particles with spin 3/2

The paper gives a derivation of a full system of wave equations for particles with spin 3/2.

The relativistic theory of particles with maximum spin I

The paper deals with the structure of linear relativistic wave equations for particles with maximum spin 1 and with non-zero rest mass. It can be proved that the only permissible equations for these particles are the known Dirac equations for the electron and the equations for scalar and vector (pseudo-scalar and pseudovector) meson fields.

On relativistic wave equations for particles of arbitrary spin in an electromagnetic field

The investigations of Dirac (1936) on relativistic wave equations for particles with arbitrary spin have recently been followed up by one of us (Fierz, 1939, referred to as (A)) It was there found possible to set up a scheme of second quantization in the absence of an external field, and to derive expressions for the current vector and the energy-momentum tensor. These considerations will be extended in the present paper to the case when there is an external electromagnetic field, but we shall in the first instance disregard the second quantization and confine ourselves to a c -number theory. The difficulty of this problem is illustrated by the fact that the most immediate method of taking into account the effect of the electromagnetic field, proposed by Dirac (1936), leads to inconsistent equations as soon as the spin is greater than 1.