Ian J R Aitchison

Gauge theories in particle physics : a practical introduction

Experimental and theoretical elements - quarks and leptons and the forces between them electromagnetism as a gauge theory the Klein-Gordon and Dirac wave equations and the interpretation of their negative energy solutions quantum field theory quantum electrodynamics - the electromagnetic interactions of spin-O particles forces and particle exchange processes the electromagnetic interactions of spin-1/2 particles deep inelastic electron-nucleon scattering and the quark parton model non-abelian gauge theory an introduction to quantum chromodynamics phenomenology of weak interactions - introduction to weak interactions the hadronic weak current and neutral currents difficulties with weak interaction phenomenology theory of electroweak interactions hidden gauge variance - the U(1) case the Glashow-Salam-Weinberg theory of electroweak interactions.

Supersymmetry in particle physics : an elementary introduction

1. Introduction and motivation 2. Spinors: Weyl, Dirac and Majorana 3. A simple supersymmetric Lagrangian, and a first glance at the MSSM 4. The supersymmetry algebra and supermultiplets 5. The Wess-Zumino model 6. Superfields 7. Vector (or gauge) supermultiplets 8. The MSSM 9. SUSY breaking 10. The Higgs sector and electroweak symmetry breaking in the MSSM 11. Sparticle masses in the MSSM 12. Some simple tree-level calculations in the MSSM References Index.

Failure of the derivative expansion for studying stability of the baryon as a chiral soliton

Abstract We investigate whether the terms in the derivative expansion up to and including (ϖφ) 6 provide a useful local approximation to the one fermion loop effective action of the SU(2) chiral model, for the purpose of discussing soliton stability. By comparing the contribution of these terms to the static energy with the exact evaluation of the complete one-loop (Casimir) energy, we conclude that the derivative expansion does not provide a useful approximation for discussing stability of the soliton at sizes relevant to nucleon physics.

Diffraction dissociation, the deck mechanism and diffractive resonance production

Abstract We have constructed a model amplitude for the diffractive production of resonant states in the presence of Deck amplitudes: rescattering corrections to the Deck amplitudes are included. We have found that gross distortion of the resonance may occur and also that the phase of the diffractively produced system may vary very slowly, despite the existence of resonances: the only requirement is that the phase of the Deck amplitude leads the production phase of the resonance by ≈40°. Our model simultaneously accommodates the well established lack of phase variation in the diffractively produced 1 + s-wave (A1) ϱπ system and the details of the variation of intensity with mass, with resonance parameters M A1 ≈ 1.3 GeV/ c 2 and Γ A1 ≈ 240 MeV/ c 2 . The analogous Kππ (Q) diffractive enhancement fits satisfactorily into the same framework. Our model also accounts for a number of features of diffractive N ∗ production.

Understanding Heisenberg’s “magical” paper of July 1925: A new look at the calculational details

In July 1925 Heisenberg published a paper that ushered in the new era of quantum mechanics. This epoch-making paper is generally regarded as being difficult to follow, partly because Heisenberg provided few clues as to how he arrived at his results. We give details of the calculations of the type that Heisenberg might have performed. As an example we consider one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. The results are precisely those obtained in standard quantum mechanics, and we suggest that a discussion of the approach, which is based on the direct calculation of transition frequencies and amplitudes, could usefully be included in undergraduate courses on quantum mechanics.

Inverse Landau-Khalatnikov transformation and infrared critical exponents of (2+1)-dimensional quantum electrodynamics

Abstract By applying an inverse Landau-Khalatnikov transformation, connecting (resummed) Schwinger-Dyson treatments in non-local and Landau gauges of QED 3 , we derive the infrared behaviour of the wave-function renormalization in the Landau gauge, and the associated critical exponents in the normal phase of the theory (no mass generation). The result agrees with the one conjectured in earlier treatments. The analysis involves an approximation, namely an expansion of the non-local gauge in powers of momenta in the infrared. This approximation is tested by reproducing the critical number of flavours necessary for dynamical mass generation in the chiral-symmetry-broken phase of QED 3 .

Stable soliton solution of the CP1 model with a Chern-Simons term

Abstract A stable (finite size, finite energy) static soliton, of unit winding number, is found numerically in the CP 1 model with a Chern-Simons (CS) term. The size is of order 4k ⨍ , where k is the CS coefficient and ⨍ is the CP 1 mass scale. The energy is approximately 1.035 in units of 2π⨍. A possible application to P -and T -violating spin liquids is suggested.

A two-resonance analysis of the Q (Kππ) enhancement

We have constructed a model of the Q enhancement in Kππ spectra in which the Q is regarded as dominated by diffractive production of two 1+ mesons. We show that our model accounts satisfactorily for the Kππ mass spectrum in the Q region and for the relative amounts of ϱK and K∗π as a function of mass. Regarding the A1 phenomenon as a diffractively produced meson, we find our derived parameters yield values of the A1 and B widths in accord with experiment, and study their implications for the A1 nonet. We also make predictions concerning Q production through strangeness and charge exchange.

Relativistic Quantum Mechanics

The Special Theory of Relativity was already firmly established when quantum mechanics was discovered in 1925, so it was understood that if a fundamental theory purported to supercede classical mechanics it must be Lorentz covariant. At that time, the only known “elementary” particles were the photon, electron and proton. Construction of a relativistic theory of photons was accomplished rather quickly by Dirac — in effect, by canonical quantization of Maxwell’s expression for the energy of the electromagnetic field, as described in §10.1. In atomic and molecular phenomena, protons move so slowly that no one was concerned with their high velocity behavior until much later. On the other hand, that relativistic corrections to the Bohr model of hydrogen can account for the fine structure of hydrogenic spectral lines had been demonstrated by Sommerfeld in 1916. For that reason, the search for a relativistic, quantum mechanical description of electrons began immediately. This, however, proved to be a far more difficult task than the quantization of the electromagnetic field.

Spurious nature of certain unitarity corrections to the isobar model for three hadron final states

Abstract Various methods of implementing unitarity corrections to the isobar model for three hadron final states are discussed, and it is explained why some lead to spurious effects because insufficient attention is paid to analyticity. Recent calculations of unitarity corrections in the processes A1 → πππ and πN → ππN are shown to contain spuriously large effects. This may explain why fits to the first process were worsened when these corrections were included.