Non-relativistic current algebra in the N/V limit

Goldin, Gerald A.; Grodnik, J.; Powers, Robert T.; Sharp, David H.

doi:10.2172/4344130

Cited by 13 publications

(14 citation statements)

References 5 publications

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“…HIP 39681 (HD 66948, G5IV, 68 pc) is a single-lined binary with a long 4.7-yr period. Astrometric orbit with similar period has been published by Goldin & Makarov (2007). The large minimum secondary mass, 0.5 M ⊙ , indicates that the RV amplitude could be reduced by line blending.…”

Section: Comments On the Individual Objectssupporting

confidence: 69%

Spectroscopic orbits of nearby stars

Sperauskas

Deveikis

Tokovinin

2019

A&A

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Aims. We observed stars with variable radial velocities to determine their spectroscopic orbits. Methods. Velocities of 132 targets taken over a time span reaching 30 years are presented. They were measured with the correlation radial velocity spectrometers (1913 velocities) and the new VUES echelle spectrograph (632 velocities), with typical accuracy of 0.5 and 0.2 km s −1 , respectively. Results. We derived spectroscopic orbits of 57 stars (including 53 first-time orbits), mostly nearby dwarfs of spectral types K and M. Their periods range from 2.2 days to 14 years, some of those are Hipparcos astrometric binaries. Comments on individual objects are provided. Many stars belong to hierarchical systems containing three or more components, including 20 new hierarchies resulting from this project. The preliminary orbit of the young star HIP 47110B has a large eccentricity e = 0.47 despite short period of 4.4 d; it could be still circularizing. Conclusions. Our results enrich the data on nearby stars and contribute to a better definition of the multiplicity statistics.

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Section: Comments On the Individual Objectssupporting

confidence: 69%

Spectroscopic orbits of nearby stars

Sperauskas

Deveikis

Tokovinin

2019

A&A

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“…20 other boundary conditions were used for this purpose.). We will assume we already know that the generating functional for a Free Bose Gas satisfies the equation, …”

Section: Appendixmentioning

confidence: 99%

Hamiltonian and generating functional for a non-relativistic local current algebra

Menikoff¹

1974

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“…22 It is important to have a unified framework in which all of these representations can be studied. In a later paper, representations will be obtained which describe infinitely many identical particles, at a constant average density.…”

Section: J T)-+ (Jo'-\l To '-\I)mentioning

confidence: 99%

Nonrelativistic Current Algebras as Unitary Representations of Groups

Goldin

1971

Journal of Mathematical Physics

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It is possible that a complete physical theory can be written entirely in terms of operators such as current densities, rather than in terms of field operators. The current densities in these models correspond in general to distributions of unbounded operators. Such a theory is reviewed for the case of nonrelativistic quantum mechanics. It is found that one can exponentiate the current algebra to obtain a group, which may then be represented by unitary (hence bounded) operators in Hilbert space. This procedure is analogous to exponentiating the canonical commutation relations and obtaining the Weyl group. For nonrelativistic quantum mechanics without spin, the group is the semidirect product J A .K Schwartz space J(IP. ") with a group J" of certain C cf.) dilfeomorphisms from fR 3 onto itself.For fEJ and cp E3\;, the composition mapping <.r,cp) -+focp defines the semidirect product law.The Gel'fand-Vilenkin formalism for "nuclear Lie groups" is suitable for the representation theory of such a group. Almost all of the physical information is contained in a cylindrical measure f1 on J', the dual of the nuclear space J. The Fourier transform of It can be interpreted as an expectation functional with respect to the state of lowest energy. The nonrelativistic Fock representation (including the theory of n particles in a box) is examined in this formalism. Conditions on f1 are systematically developed which suffice to recover all of the infinitesimal generators on a common, dense, invariant domain in the Hilbert space. For the Weyl group slightly weaker conditions than for the semidirect product case would suffice. Gaussian measures in J', as well as the measures defining n-particle representations of J A X, satisfy these conditions.

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Non-relativistic current algebra in the N/V limit

Cited by 13 publications

References 5 publications

Spectroscopic orbits of nearby stars

Spectroscopic orbits of nearby stars

Hamiltonian and generating functional for a non-relativistic local current algebra

Nonrelativistic Current Algebras as Unitary Representations of Groups

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