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This paper presents the necessary and sufficient conditions that a Riemannian geometry have as its source a real or complex massive scalar field.
The kinematic singularities and threshold relations of helicity amplitudes for inelastic pion‐nucleon scattering involving higher baryons in the final state are discussed. A recipe for writing the s ‐ and t ‐ channel helicity amplitudes is obtained using Wigner‐Bargmann formalism....
A procedure for quantization is given which does not require the canonical formalism. Only the equation of motion for the field and the resulting conserved current are needed to derive all the necessary commutators or anticommutators, the operators which represent the physical observables, the...
It is shown that the ``new symmetry'' of Racah coefficients, recently derived in a paper by Minton J. Math. Phys. 11 , 3061 (1970), does not exist.
Prolate‐spheroidal expansions of the spin‐orbit, spin‐spin, and orbit‐orbit operators are derived. These expansions are analogs of the Neumann expansion for 1∕ r 12 and can be used to study the corresponding exchange interactions in diatomic molecules.
Contributions of baryon poles of spin J to the π N → π N and π N → γ N amplitudes have been calculated using the Wigner‐Bargmann formalism. An ambiguity arising from off‐the‐mass‐shell continuation of the propagator has been discussed and a continuation which gives pure spin‐ J...
We prove the existence of phase transitions in several kinds of two‐component lattice gases: Some of these are isomorphic to spin systems and∕or to fluids composed of asymmetrical molecules which can have different orientations. Among the models studied is one with infinite repulsion between...
The interaction Hamiltonian λ ∫ : (0) ( x ) ψ (0) ( x ): g ( x ) d s x , g ( x ) ∊ S ( R s ) λ ∫ : ψ ̄ ( 0 ) ( x ) ψ ( 0 ) ( x ) : g ( x ) d s x , g ( x ) ∊ S ( R s ) is studied. An ultraviolet cutoff is introduced. We remove this cutoff, and take the limit g → 1 in S ( R s ) S (...
Harrison's 40 space‐time metrics have been checked to see if they represent vacuum solutions. Four of them are found to be nonvacuum. The Petrov classification is found for all the metrics, and those of type D are placed in their (invariantly defined) Kinnersley classes.
A method of obtaining the explicit form of the gravitational field of multipoles in the second approximation is furnished here. The generalization of this method to any superposition of multipoles is straight‐forward. We obtain as an example the second‐order metric for the superposition of a...
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