Anti-particles

Abstract. The Dirac equation is discussed in a semiclassical context, with an emphasis on the separation of particles and anti-particles. Classical spin-orbit dynamics are obtained as the leading contribution to a semiclassical approximation of the quantum dynamics. In a second part the propagation of coherent states in general spin-orbit coupling problems is studied in two different semiclassical scenarios. 

Our approach is based on a systematic semiclassical study of the Dirac equation. After separating particles and anti-particles to arbitrary powers in h, a semiclassical expansion of the quantum dynamics in the Heisenberg picture is developed. To leading order this method produces classical spin-orbit dynamics for particles and anti-particles, respectively, that coincide with the findings of Rubinow and Keller Hamiltonian relativistic (anti-) particles drive a spin precession along their trajectories. A modification of that method leads to a semiclassical equivalent of the Foldy-Wouthuysen transformation resulting in relativistic quantum Hamiltonians with spin-orbit coupling. 

In order to achieve a semiclassical separation of particles and anti-particles one starts with the projection matrices... 

Note that the projection operator P = (1 a, vF)/2 projects out the particle state, wF, and the anti-particle state, ip- (or more preciselyip-), from the Dirac spinor field k. The quasi-quarks in a patch carries the residual momentum l1 and is given as... 

We see that the modes near the Fermi surface contributes only some parts of the axial anomaly. As in the vector current, the rest should come from modes in the deep Fermi sea and from anti-particles. To recover the full axial anomaly we add a counter term (See Fig. 7), which is two thirds of the axial anomaly plus a Chern-Simons term ... 

This inevitably leads to the annihilation of anti-particles from the bound states of protonium (Pn = pp) and positronium (Ps = e+e ). We found this reaction to be a very important mechanism for the loss of antihydrogen [26, 27, 29]. 

THIRTY YEARS THAT SHOOK PHYSICS The Story of Quantum Theory, George Gamow. Lucid, accessible introduction to influential theory of energy and matter. Careful explanations of Dirac s anti-particles, Bohr s model of the atom, much more. 12 plates. Numerous drawings. 240pp. 5X x 8H. 24895-X Pa. 5.95... 

The present model is quite surprising in its simplicity and yet the interpretation is very different compared to classical and quantum mechanical pictures. The ansatz Eq. (2) implies that every fundamental quantum particle will occupy one of two quantum states. When the choice is made the associated antiparticle will be indirectly recognized through the kinematical interaction v and the appearance of the length- and time-scale contractions. We do not, therefore, directly experience mirror- (anti-)particles, unless they are bodily excited. Within the present description, we have proposed a generalized quantum description, which transcends classical features as the contraction of scales mentioned above, including also a dynamical formulation of gravitational interactions. 

The first anti-particle discovered was the anti-electron, the so-called positron, in 1933 by Anderson [3] in the cloud chamber due to cosmic radiation. The existence of the anti-electron (positron) was described by Dirac s hole theory in 1930 [4], The result of positron—electron annihilation was detected in the form of electromagnetic radiation [5]. The number and event of radiation photons is governed by the electrodynamics [6, 7]. The most common annihilation is via two- and three-photon annihilation, which do not require a third body to initiate the process. These are two of the commonly detected types of radiation from positron annihilation in condensed matter. The cross section of three-photon annihilation is much smaller than that of two-photon annihilation, by a factor on the order of the fine structure constant, a [8], The annihilation cross section for two and three photons is greater for the lower energy of the positron—electron pair it varies with the reciprocal of their relative velocity (v). In condensed matter, the positron—electron pair lives for only the order of a few tenths to a few nanoseconds against the annihilation process. 

Entities that move in the interface are achiral and massless. A virtual photon consists of a virtual particle/anti-particle pair. The vector bosons that mediate the weak interaction are massive and unlike photons, distinct from their anti-particles. The weak interaction therefore has reflection symmetry only across the vacuum interface and hence /3-decay violates parity conservation. 

The positron was the first anti-particle to be discovered. Every elementary particle is now known to have a corresponding... 

Anti-proton—The anti-particle of the proton. Identical to the proton except that its charge is opposite in sign. 

A number of particles with properties opposite in some respect to those mentioned are known, for instance the positron (electron) and the antiproton. More of these anti-particles are likely to be observed when the high power ( 10 eV) accelerators come into operation. 

When an electron and a positron, its anti particle, meet, they are annihilated and are completely transformed into energy, mostly y radiation. 

Matter and antimatter ) There s an intriguing analogy between bifurcations of fixed points and collisions of particles and anti-particles. Let s explore this in the context of index theory. For example, a two-dimensional version of the saddle-node bifurcation is given by x = a + x, y = -y, where a is a parameter. 

Quantum mechanics has to a large extent resolved an antinomy inherited from the discussions of Heraclit and Democrit. The wave-functions are continuous and extended in the former sense, but at the same time, the indivisible parts of Democrit have been replaced by normalization conditions, the numbers K, Z, N,.. . of electrons, protons, neutrons,.. . being cardinal numbers without any possible way of assigning ordinal numbers to the individual, indiscernible entities. This trend has been further accentuated by most particles having anti-particles, with exception of some bosons (such as the photon and the neutral pion, but not the a-particle). 

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