Representations of Local Nonrelativistic Current Algebras

Grodnik, J.; Sharp, David H.

doi:10.1103/physrevd.1.1531

Cited by 24 publications

(8 citation statements)

References 11 publications

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“…23 In this example, we easily see that a/oAtis not a welldefined operator, while the sum (4.58) nevertheless is well defined. If (4.60) may be termed the "I-particle identity."…”

Section: U(f) and Vs(~) Act In L!({f X + Fx}) By The Equationsmentioning

confidence: 81%

“…Let fk = 2m c~f(m) ' We shall show that lim (F,fk) = 0 as k -00, where (F,h) is defined from A by the formula where M denotes the operation of pointwise multiplication. 23 Thus the representation (4.57) is also a general form; the specific choice of representation is made when a cylindrical measure quasi-invariant under the group 'ill is placed on {A}. 23 Thus the representation (4.57) is also a general form; the specific choice of representation is made when a cylindrical measure quasi-invariant under the group 'ill is placed on {A}.…”

Section: U(f) and Vs(~) Act In L!({f X + Fx}) By The Equationsmentioning

confidence: 99%

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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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“…23 In this example, we easily see that a/oAtis not a welldefined operator, while the sum (4.58) nevertheless is well defined. If (4.60) may be termed the "I-particle identity."…”

Section: U(f) and Vs(~) Act In L!({f X + Fx}) By The Equationsmentioning

confidence: 81%

Section: U(f) and Vs(~) Act In L!({f X + Fx}) By The Equationsmentioning

confidence: 99%

Nonrelativistic Current Algebras as Unitary Representations of Groups

Goldin

1971

Journal of Mathematical Physics

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“…The general idea of using current operators as collective coordinates of a non-relativistic system goes back to early hydrodynamic studies of Landau [27]. This problem was reformulated at the end of the sixties as a non-relativistic current algebra [29][30][31][32][33][34]. Currents can be considered as the fundamental dynamical variables rather than the underlying canonical fields.…”

mentioning

confidence: 99%

“…The mathematical foundation for the non-relativistic current algebra has been developed in [29][30][31][32][33][34]. The main emphasis of this type of theory is the algebraic structure of the equal-time current-current commutation relations.…”

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confidence: 99%

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Vortex waves on a nuclear surface

Kartavenko

Maruhn

Greiner

1996

J. Phys. G: Nucl. Part. Phys.

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In heavy-ion collisions a localized stable or long lived excitation might develop. The existence of a fairly well defined nuclear surface makes it possible to discuss localized excitations in the nuclear surface region. In the framework of semiclassical nonlinear nuclear hydrodynamics we have presented a type of vortical excitation that are new in nuclear physics. We have found a class of uniformly rotating solutions to nonlinear Euler-type equations on a sphere. The equations of motion describing a localized vortex on a spherical nuclear surface-a bounded region of constant vorticity, surrounded by irrotational flux-are derived. The qualitative analysis of the main properties of this vortex is presented. These excitations may be linked with hot spots created in peripheral heavy-ion collisions.

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Diffeomorphism Groups And Local Symmetries: Some Applications In Quantum Physics

Goldin

Sharp

1989

Symmetries in Science III

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Representations of Local Nonrelativistic Current Algebras

Cited by 24 publications

References 11 publications

Nonrelativistic Current Algebras as Unitary Representations of Groups

Nonrelativistic Current Algebras as Unitary Representations of Groups

Vortex waves on a nuclear surface

Diffeomorphism Groups And Local Symmetries: Some Applications In Quantum Physics

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