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This short note describes a technique which is useful for solving higher‐dimensional periodic systems in which a large amount of homogeneity and symmetry is absent.
We prove for Hermitian matrices (or more generally for completely continuous self‐adjoint linear operators in Hilbert space) A and B that Tr ( e A+B ) ≤ Tr ( e A e B ). The inequality is shown to be sharper than the convexity property (0 ≤ α ≤ 1) Tr ( e α A +(1−α) B ) ≤ Tr ( e A )...
The Muskhelishvili method is used to obtain the off‐the‐mass‐ shell V — θ scattering amplitude.
Formulas are obtained which give the matrix representation, relative to a product basis, of the projection operator for the total angular momentum of a system. If the individual angular momenta are not too large, the matrix elements depend upon a small number of parameters, independent of the...
In the framework of the Haag‐Ruelle collision theory one‐particle singularities are proved to exist in the physical region of any connected scattering amplitude. They occur with the causal propagator ( p 2 − m 2 + i ϵ) −1 in the dominant term and have a residue, which factors into the...
Starting from their generating functional, we investigate the structure of the finite and divergent parts of propagators in quantum electrodynamics. A renormalizability condition is expressed by means of a set of recursion formulas between the finite parts of radiative corrections of the...
This paper is concerned with multipole structure for the sources of the gravitational field in the full (axially symmetric) nonlinear gravitational theory. Definitions proposed recently by Janis and Newman for the mass of the source, its linear momentum, dipole moment, and its spin or angular...
A crossing symmetric Regge representation for the invariant scattering amplitude is constructed which simultaneously exhibits all Regge poles in the three channels. It is assumed that the amplitude satisfies the Mandelstam representation, and that the usual Mandelstam‐Sommerfeld‐Watson...
It is possible to quantize most classical field theories by identifying the group of canonical transformations which maintain the covariance properties with a group of unitary transformation in Hilbert space which has the same commutator algebra. The commutators among the canonical field...
A new method is introduced to find properties of wave and other fields. The relationship between the geometry of the strip and the symmetry of the Helmholtz equation is shown and leads to previously undiscovered properties of the field. The field pattern of the strip is shown to have a...
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