On the Relationship of Quantum Mechanics to Classical Electromagnetism and Classical Relativistic Mechanics

Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz Equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as `inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalisation to massive particles leads to the Klein--Gordon and Schr\"{o}dinger Equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.Comment: 14 pages, no figures, no table

Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. This formalism, making essential use of the 4-vector electromagnetic potential concept, provides a short derivation of the Lorentz force law of classical electrodynamics, the conventional definition of the magnetic field, in terms of spatial derivatives of the 4--vector potential and the Faraday-Lenz Law. An important distinction between the physical meanings of the space-time and energy-momentum 4--vectors is pointed out.Comment: 15 pages, no tables 1 figure. Revised and extended version of physics/0307133 Some typos removed and minor text improvements in this versio

A Study of the LEP and SLD Measurements of AbA_b

A systematic study is made of the data dependence of the parameter $A_{\rm{b}}$, that, since 1995, has shown a deviation from the Standard Model prediction of between 2.4 and 3.1 standard deviations. Issues addressed include: the effect of particular measurements, values found by individual experiments, LEP/SLD comparison, and the treatment of systematic errors. The effect, currently at the 2.4$\sigma$ level, is found to vary in the range from 1.7$\sigma$ to 2.9$\sigma$ by excluding marginal or particularly sensitive data. Since essentially the full LEP and SLD Z decay data sets are now analysed the meaning of the deviation, (new physics, or marginal statistical fluctuation) is unlikely to be given by the present generation of colliders.Comment: 15 pages 7 figures 7 table

Fitting Precision Electroweak Data with Exotic Heavy Quarks

The 1999 precision electroweak data from LEP and SLC persist in showing some slight discrepancies from the assumed standard model, mostly regarding $b$ and $c$ quarks. We show how their mixing with exotic heavy quarks could result in a more consistent fit of all the data, including two unconventional interpretations of the top quark.Comment: 7 pages, no figure, 2 typos corrected, 1 reference update

New Axial Interactions at a TeV

We consider a heavy fourth family with masses lying in the symmetry breaking channel of a new strong gauge interaction. This interaction generates a heavy quark axial-type operator, whose effects can be enhanced through multiple insertions. In terms of the strength of this operator we can express new negative contributions to the S and T parameters and the shifts of the Z couplings to the third family. In particular we find that the new contribution to T is strongly constrained by the experimental constraints on the Z coupling to the tau.Comment: 14 pages, 1 figure, PRD versio

Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD

The one-loop QCD effective charge $\alpha_s^{eff}$ for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitary covariant gauge. Except for the particular choice of gauge parameter $\xi = -3$, $\alpha_s^{eff}$ is found to {\it increase} with increasing physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $\xi = -3$, $\alpha_s^{eff}$ decreases with increasing $Q$ and satisfies a renormalisation group equation. Also, except for the case $\xi = 19/9$, convergence radii of geometric series are found to impose upper limits on $Q$.Comment: 28 pages, 5 tables, 5 figures. v3 The one-loop amplitudes in Section 2 are recalculated using dimensional regularisation, and several errors in the on-shell calculation of Reference[1] are pointed out. v4 one figure removed one added. Three tables and new text in Section 5 added. Published versio

The Experimental Status of the Standard Electroweak Model at the End of the LEP-SLC Era

A method is proposed to calculate the confidence level for agreement of data with the Standard Model (SM) by combining information from direct and indirect Higgs Boson searches. Good agreement with the SM is found for $m_H \simeq 120$ GeV using the observables most sensitive to $m_H$: $A_l$ and $m_W$. In particular, quantum corrections, as predicted by the SM, are observed with a statistical significance of forty-four standard deviations. However, apparent deviations from the SM of 3.7$\sigma$ and 2.8$\sigma$ are found for the Z$\nu \bar{\nu}$ and right-handed Zb$\bar{{\rm b}}$ couplings respectively. The maximum confidence level for agreement with the SM of the entire data set considered is $\simeq 0.006$ for $m_H \simeq 180$ GeV. The reason why confidence levels about an order of magnitude higher than this have been claimed for global fits to similar data sets is explained.Comment: 47 pages, 8 figures, 24 tables. An in-depth study of statistical issues related to the comparison of precision EW data to the S

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the $\beta$ function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.Comment: 4 pages, Revtex - Added some clarifying comments and new reference

Mass and Coupling Constant Limits from Convergence Conditions on the Effective Charge in QED

The massless fermion limit of QED is discussed. For on-shell renormalisation the high energy behaviour fixes no lower limit on the mass of the lightest fermion if the fine structure constant $\alpha$ is allowed to vary. The choice of an arbitary (space-like) subtraction point does, however, fix a lower limit on the mass of the lightest fermion, for any subtraction scale $\mu$, if the effective charge \aefmu respects both quantum mechanical superposition and renormalisation scale invariance. Limits on the values of $\alpha$ or the electron mass are obtained within the Standard Electroweak Model by requiring convergence of \aefmz.Comment: 18 pages, 3 tables 4 figure

The Indirect Limit on the Standard Model Higgs Boson Mass from the Precision FERMILAB, LEP and SLD Data

Standard Model fits are performed on the most recent leptonic and b quark Z decay data from LEP and SLD, and FERMILAB data on top quark production, to obtain $m_t$ and $m_H$. Poor fits are obtained, with confidence levels $\simeq$ 2%. Removing the b quark data improves markedly the quality of the fits and reduces the 95% CL upper limit on $m_H$ by $\simeq$ 50 GeV.Comment: 6 pages 3 tables i figur