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Elementary Theory of Angular Momentum
01 Dec 1957-
About: The article was published on 1957-12-01 and is currently open access. It has received 3550 citations till now. The article focuses on the topics: Total angular momentum quantum number & Angular momentum of light.
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TL;DR: In this paper, a single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer.
Abstract: A single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer. A state of mixed spin symmetry and lowered space symmetry is constructed which has both conceptual and practical computational value. Either unrestricted Hartree–Fock theory or spin polarized density functional theory, e.g., Xα theory, can be used to generate the mixed spin state wave function. The most important consequence of the theory is that the Heisenberg exchange coupling constant J can be calculated simply from the energies of the mixed spin state and the highest pure spin multiplet.
2,242 citations
26 May 1995
TL;DR: In this paper, a reasonably connected outline of quantum field theory is given, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.
Abstract: Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.
1,567 citations
TL;DR: In this article, the general analysis of binary reactions involving particles with arbitrary spin is reformulated in such a way, that it applies equally well to relativistic particles (including photons).
Abstract: The general analysis of binary reactions involving particles with arbitrary spin is reformulated in such a way, that it applies equally well to relativistic particles (including photons). This is achieved by using longitudinal spin components (“helicity states”) not only in the initial and final states, but also in the angular momentum states which are employed as usual to reduce the S-matrix to a simpler form. Expressions for the scattering and reaction-amplitude, intensity and polarization are given. They involve fewer vector-addition coefficients than the customary formulas, and no recoupling coefficients. The application to some examples is sketched, and in the Appendix some formulas are given that may be of use in the applications.
1,447 citations
Cites background from "Elementary Theory of Angular Moment..."
...If j=l, an integer, one can start from d l00 , or more generally d lm0 , see Table I, and calculate d l m1 , d l m2 , ..., by means of the recursion formula (A4) or alternatively by using 14 Our notations follow Rose's book; in particular Plm(3)=e&im,Ylm(3,)....
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...15 See for example Rose [17], equation preceding (4.26) or Edmonds [18, Eq....
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...15 See for example Rose [17], equation preceding (4....
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...We refer the reader to Wigner's [9] and other well-known books [17, 18](14) for more extensive information....
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TL;DR: In this article, the authors define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish, and define chiral vertex operators and duality matrices and review the fundamental identities they satisfy.
Abstract: We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.
1,305 citations
Cites background from "Elementary Theory of Angular Moment..."
..." (The completeness of these equations for the 6j symbols of SU(2) was first proven by Racah [36]....
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...For example, in the case of 5(7(2), the pentagon identity is known as the "Biedenharn sum rule" [36], In more detail, one usually chooses a basis for the representation space by diagonalizing J3 in the Cartan subalgebra: {[/',m>}, m=—j,....
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TL;DR: In this article, it was shown that the distortion of the hydrated complex by collisions with other water molecules is responsible for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields.
Abstract: The proton relaxation time in solutions of paramagnetic ions depends, among other factors, on the relaxation time of the electron spins, τs. It is shown that the latter, for ions of the iron group, is determined mostly by the distortion of the hydrated complex by collisions with other water molecules. The theory provides a quantitative explanation for the decrease in T2 in Mn++ (and other) solutions in very high magnetic fields. The experimentally observed field and temperature dependence of the proton relaxation times, T1 and T2, for ions of the iron group is compared with theory and the features which depend on τs are stressed.
1,192 citations