Schwinger Formalism Research Articles

On the Schwinger variational principle in electron-atom scattering

It is shown that for S-S atomic transitions the Schwinger variational principle with sufficiently flexible one-state functions does not take account of long-range polarization effects, even though the Schwinger formalism explicitly contains long-range terms. The plane-wave (1,1) Pade approximant to an S to S transition in general exhibits long-range behaviour. However since this approximant is obtained by applying the Schwinger principle to rather restricted one-state trial functions its accuracy must be called into question.

Weak Radiative Decays of Hyperons in the Pole Model

It is found that the pole model which includes the decuplet pole contributions in the weak radiative decays of hyperons fails to give the correct sign of the Σ+ → pγ asymmetry parameters α, although the magnitude of the decay rate and of α are consistent with the present experimental data. This conclusion holds in the Rarita–Schwinger formalism. Earlier calculations are incorrect due mainly to an error in the spin-3/2 propagator used in the theory, and inconsistencies in the SU(3) phase convention.

The many-body problem in terms of particle group functions

In the treatment of many-particle systems the particle correlations can be taken into account to a certain extent at the very beginning by choosing particle-group basis functions. However, when these basis functions do not satisfy a certain restrictive condition (“strong orthogonality”) some mathematical difficulties arise. Using a previously discovered way of overcoming these difficulties [3] we develop practical methods to solve this problem. The Green’s function formalism of Martin and Schwinger is applied using field operators for the particle groups with intrinsic degrees of freedom. Besides the possible computational advantages and the intrinsic interest of the problem this theory yields some possibilities for an ab initio microscopic theory of condensed media. In addition, it can also be useful in throwing light on some questions of relativistic field theory of structured particles.

Algebraic Aspects of Trilinear Commutation Relations

An attempt is made to derive from the formalism of Schwinger's action principle, in a more convincing manner than previously described, a set of trilinear equal-time commutation relations which contains the commutation relations first discussed by H. S. Green as special cases. Matrix representations of field operators satisfying the trilinear commutation relations are considered. Two representations are explicitly discussed: a four-dimensional and an eight-dimensional representation. The representations considered and the bilinear equal-time commutation relations between the associated ``component fields'' obeying ordinary statistics are specified by irreducible representations of an algebra which is suggested by the trilinear commutation relations. The component fields associated with the same representation and of the same spin differ from each other in their bilinear equal-time commutation relations with other fields. This difference is reflected in the interactions into which the various fields can enter.

Surface Properties of Ground-State Nuclear Matter

A general method is derived for extending the many-body formalism of Martin and Schwinger to macroscopic inhomogeneous systems. This method is applied to the Puff-Martin approximation for nuclear matter and used to compute the properties of a plane nuclear surface. An iterative self-consistency computation is used, and a generalized effective-mass approximation is imposed to simplify the wave equation. The particle interaction is taken to be a separable Yamaguchi potential with an $S$-state hard shell. The results show a smoothly varying density and self-energy, with a surface thickness of 2.33 F. A calculation of the surface energy term in the Weizs\"acker semiempirical mass formula gives 18.79 MeV.

Initial value data for poisson brackets in general relativity

As a preliminary step toward constructing the commutators of a quantized theory of general relativity, Poisson brackets for the classical theory are found on an initial space-like surface. These can then be extended over all space-time by solving the equations of motion. The theoretical structure used to find the brackets is an extension of the formalism of Schwinger. The brackets obtained are determined only up to a gauge transformation.

Zero-energy Mesonic Processes and Renormalization in Schwinger's Formalism

Zero-energy Mesonic Processes and Renormalization in Schwinger's Formalism

On the Transition Matrix and the Green Function in the Quantum Field Theory

The J. Schwinger's formalism of the Green function in the quantum electrodynamics is applied to the transition problem of the state. It is shown that the many body kernel in the Heisenberg representation involves the information about the transition of the state and this is dh'ectly represented by the repeated use of the one body kel'Oel G,@ and the vertex opel'ator rlL defined by J. Schwinger. Further, the renormalization is discussed without use of the usual perturbation theory, although then: remains the difficulty associated with the b-divergence.

The Hyperfine Structure of Hydrogen

The two-body formalism of Schwinger is modified to consider the case of the hydrogen atom. The proton's anomalous moment is treated by adding a Pauli-type term to the Lagrangian. A perturbation theory based upon the Green's function is developed and the first-order correction to the Fermi hyperfine splitting of the ground state is calculated. The method of calculation used is that of Karplus and Klein in their positronium work. Aside from the usual renormalizations encountered, an extra infinity appears in the calculation associated with the assumption of a point anomalous magnetic moment for the proton. On the hypothesis that the proton's moment is actually distributed, cutoffs are inserted. The modified hyperfine formula leads to a new value of $\ensuremath{\alpha}:\frac{1}{\ensuremath{\alpha}}=137.0378$ for a cutoff at the meson length and $\frac{1}{\ensuremath{\alpha}}=137.0374$ for a cutoff at the proton length.

The Self-Stress of the Electron

The diagonal elements of the symmetrical energy-momentum tensor density of an electron at rest are calculated. The covariant formalism of Tomonaga, Schwinger, Feynman, and Dyson is used, and it is shown that it is necessary to use a relativistic cut-off in addition to the covariant separation of the infinite renormalizations. Therefore "formalistic regulators" are used in the form of additional neutral vector fields. The integrations are carried out with the Feynman method. The resultant vanishing value for the self-stress constitutes a proof of the consistency of the relativistic formalism. It is also shown how the Feynman-Dyson method can be used for the calculation of expectation values of operators, of which the self-stress calculation constitutes an example.