Search Results (11 total)

We study at finite temperature the Green function and energy-momentum tensor T_μν(x) of a spinor field in 1+1 dimensions, interacting with a static background electric field. T_μν separates into a UV divergent part representing the virtual sea, and a UV finite part describing the thermal plasma of the spinor field. From T_μν we find that the virtual sea remains uniform in the presence of a uniform electric field E, while the thermal plasma becomes position dependent. This remarkable property of the thermal plasma is found to be related to the topological properties of the manifold, and to the presence of zero modes.

In quantum field theory with confining ‘‘hard’’ (e.g., Dirichlet) boundaries, the latter are represented in the Schrödinger equation defining spatial quantum modes by infinite step-function potentials. One can instead introduce confining ‘‘soft’’ boundaries, represented in the mode equation by some smoothly increasing potential function. Here the global Casimir energy is calculated for a scalar field confined by harmonic-oscillator (HO) potentials in 1, 2, and 3 dimensions. Combinations of HO and Dirichlet boundaries are also considered. Some results differ in sign from comparable hard-wall ones.

Confined equilibrium quantum gases are mor complicated than standard theory suggests. Blackbody radiation and other quantum gases in free space are uniform everywhere. However when confined by a boundary to some region of space they become nonuniform—a function of position with respect to the boundary. Standard theory based on the heat kernal expansion distorts boundary effects into distributions defined on the boundary. Here an exact, local description of boundary effects is presented for scalar gases confined by a general boundary. Explicit calculations for boundaries with a rectangular geometry illustrate all major points.

The partition function and thermodynamic potential are calculated in arbitrary space-time dimension d for scalar and spinor fields coupled to a constant vacuum gauge potential gA₀ at finite temperature T. For d=2, 4, 6, …, closed expressions in terms of Bernoulli polynomials are obtained. This generalizes known results for d=4.

A comprehensive review of the known classical solutions of SU(2) gauge theories is presented. The author follows the historical development of this subject from its beginning (the first explicit solution found was an imbedded Abelian static Coulomb solution) up to the most recent work in the field (in particular the solutions which represent monopoles, instantons, and merons). As well as being a detailed survey, this article is intended to serve as a self-contained introduction to the subject.

A comprehensive review of the known classical solutions of SU(2) gauge theories is presented. The author follows the historical development of this subject from its beginning (the first explicit solution found was an imbedded Abelian static Coulomb solution) up to the most recent work in the field (in particular the solutions which represent monopoles, instantons, and merons). As well as being a detailed survey, this article is intended to serve as a self-contained introduction to the subject.

Using nucleon quark-parton distributions obtained from inclusive leptoproduction and pion quark-parton distributions obtained from theoretical arguments we show that the Drell-Yan model does not reproduce a rather pronounced feature of recent data on dilepton production in hadron-hadron collisions. The dependence of the pN cross section on longitudinal dilepton momentum is much stronger than the dependence of the πN one, and quantitative calculations show that the model does not exhibit this feature.

We extend the Pomeron-photon analogy (i.e., the idea that the couplings of Pomerons and photons to hadronic matter are similar) to vector-meson photoproduction and related processes, such as ρ electroproduction and Compton scattering. To avoid directly coupling the Pomeron to photons, which is awkward in this model, we follow conventional vector-meson-dominance ideas and approximate the photon's hadronic component by the ρ meson. We then make a current-current ansatz for the ρ elastic scattering amplitude. Spin is fully taken into account. We find that s-channel helicity conservation (SCHC) cannot be realized within this framework if the effective current is conserved; SCHC requires that either this current has a nonconserved component or the forward cross section vanishes. If an effective current with two components is introduced—one a conserved electromagnetic central component, and the other a nonconserved peripheral component—then all the main features of ρ photoproduction can be accounted for. The same model gives a good qualitative description of p p, π p, and Kp elastic scattering, and of diffractive dissociation; in other words, it provides a unified description of all diffractive phenomena. Both components of the effective current have a simple explanation in terms of the quark-parton model.

A study of the spin structure of two-body helicity amplitudes begun in a previous paper is extended to include general-mass reactions with two fermions and two bosons. The Trueman-Wick matrix joining the FB→FB and BB→FF channels (B=boson, F=fermion) is transformed into a direct sum of simple matrices M_i. The latter are 2 × 2 matrices whose elements are simple polynomials in s and t. The new s- and t-channel amplitudes related by the M_i are proportional to k.r. (kinematically regular, i.e., free from kinematic singularities and simple zeros) functions of s and t. Thus we obtain a complete set of new k.r. amplitudes for general-mass FB→FB reactions. As before, we can use the simple crossing algebra to expand the new k.r. amplitudes in terms of an elegant set of invariant amplitudes. The coefficients of these invariant amplitudes are simple functions of the crossing and scattering angles. Within a given spin class of reactions (e.g., those reactions with spins 1 / 2+0→J+0) these coefficients are also simple functions of the spins. The procedure is described by two detailed examples with FB→FB channel spins ½ + 0 → ½ + 0 and 1 / 2+0→3 / 2+0. We describe how one can achieve a general classification of invariant amplitudes based on the different kinematic roles played by different invariant amplitudes. The simplest possible connections between this classification scheme and observable dynamical situations are discussed.

The Trueman-Wick crossing matrix for general-mass BB→BB and FF→FF reactions (B=boson, F=fermion) is rearranged into a direct sum of 2 × 2 matrices whose matrix elements are simple polynomials in s and t. The s- and t-channel amplitudes related by this new matrix are proportional to k.r. (kinematically regular, i.e., no kinematic singularities or simple zeros) functions of s and t. Thus new k.r. amplitudes are constructed (simultaneously in both channels) for general-mass BB→BB and FF→FF reactions. (In addition we construct new k.r. amplitudes for general-mass BB→FF reactions.) These are not the usual "parity-conserving" k.r. amplitudes. Parity invariance is not assumed. When parity is conserved, roughly half of the new k.r. amplitudes are zero. A noncovariant procedure, based on the simplicity of the new crossing algebra, is developed for expanding the new k.r. amplitudes in terms of an elegant set of invariant amplitudes. It has the feature of very clearly relating the spin structure of a reaction to the crossing matrix for this reaction. One obtains the coefficients of invariant amplitudes as functions of the crossing angles and the particle spins. Highly ordered expressions for the spin structure are the result. This order makes possible a classification of invariant amplitudes based on the unique kinematic role played by each in the spin structure. Such a kinematic classification can be related directly to various observable dynamical situations. Should the latter occur in nature, the scheme would have dynamical content. Three examples of BB→BB reactions are given to illustrate our formalism.

The Trueman-Wick equations which connect any elastic-scattering channel with its crossed channel are, by assuming parity and time-reversal invariance in the elastic channel, decomposed into four much smaller closed systems of equations. To achieve this, new amplitudes are introduced which are certain linear combinations of helicity amplitudes. The new equations are put in a very simple factorized matrix form, and a list is given of all matrices encountered when neither spin is larger than 3 / 2. In terms of the new amplitudes, elastic-channel forward scattering constraints are of two distinct types. These are given expression for arbitrary spins. In the Regge model, one type requires conspiracy or evasion. The other type requires neither. Kinematic singularities and constraints at threshold (pseudothreshold) are discussed in terms of the new formalism.