35 research outputs found
Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach II
Extended Schwinger's quantization procedure is used for constructing quantum
mechanics on a manifold with a group structure. The considered manifold is
a homogeneous Riemannian space with the given action of isometry transformation
group. Using the identification of with the quotient space , where
is the isotropy group of an arbitrary fixed point of , we show that quantum
mechanics on possesses a gauge structure, described by the gauge
potential that is the connection 1-form of the principal fiber bundle . The coordinate representation of quantum mechanics and the procedure for
selecting the physical sector of states are developed.Comment: 18pages, no figures, LaTe
Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space
We explain in a context different from that of Maraner the formalism for
describing motion of a particle, under the influence of a confining potential,
in a neighbourhood of an n-dimensional curved manifold M^n embedded in a
p-dimensional Euclidean space R^p with p >= n+2. The effective Hamiltonian on
M^n has a (generally non-Abelian) gauge structure determined by geometry of
M^n. Such a gauge term is defined in terms of the vectors normal to M^n, and
its connection is called the N-connection. In order to see the global effect of
this type of connections, the case of M^1 embedded in R^3 is examined, where
the relation of an integral of the gauge potential of the N-connection (i.e.,
the torsion) along a path in M^1 to the Berry's phase is given through Gauss
mapping of the vector tangent to M^1. Through the same mapping in the case of
M^1 embedded in R^p, where the normal and the tangent quantities are exchanged,
the relation of the N-connection to the induced gauge potential on the
(p-1)-dimensional sphere S^{p-1} (p >= 3) found by Ohnuki and Kitakado is
concretely established. Further, this latter which has the monopole-like
structure is also proved to be gauge-equivalent to the spin-connection of
S^{p-1}. Finally, by extending formally the fundamental equations for M^n to
infinite dimensional case, the present formalism is applied to the field theory
that admits a soliton solution. The resultant expression is in some respects
different from that of Gervais and Jevicki.Comment: 52 pages, PHYZZX. To be published in Int. J. Mod. Phys.
Equivalence between Schwinger and Dirac schemes of quantization
This paper introduces the modified version of Schwinger's quantization
method, in which the information on constraints and the choice of gauge
conditions are included implicitly in the choice of variations used in
quantization scheme. A proof of equivalence between Schwinger- and
Dirac-methods for constraint systems is given.Comment: 12pages, No figures, Latex, The proof is improved and one reference
is adde
Quantum Mechanics on Manifolds Embedded in Euclidean Space
Quantum particles confined to surfaces in higher dimensional spaces are acted
upon by forces that exist only as a result of the surface geometry and the
quantum mechanical nature of the system. The dynamics are particularly rich
when confinement is implemented by forces that act normal to the surface. We
review this confining potential formalism applied to the confinement of a
particle to an arbitrary manifold embedded in a higher dimensional Euclidean
space. We devote special attention to the geometrically induced gauge potential
that appears in the effective Hamiltonian for motion on the surface. We
emphasize that the gauge potential is only present when the space of states
describing the degrees of freedom normal to the surface is degenerate. We also
distinguish between the effects of the intrinsic and extrinsic geometry on the
effective Hamiltonian and provide simple expressions for the induced scalar
potential. We discuss examples including the case of a 3-dimensional manifold
embedded in a 5-dimensional Euclidean space.Comment: 12 pages, LaTe
Manifestation of the Fermi resonance in surface polariton spectra
The method of disturbed full internal reflection (DFIR) is used to detect and interpret the resonance splitting of the surface polariton. The effect in the spectra of oscillatory SP which are reflected by the DFIR method in Otto geometry was experimentally recorded. It is concluded that the resonance splitting of the dispersion branch of SP may serve as an effective method for detecting weak oscillations and for measuring their parameters
Ограничение свобод современных подростков в процессе их самоутверждения
В статті аналізуються складові поведінкової автономії та характер контролю дорослими поведінкової свободи сучасних підлітків та юнаків.The making autonomies of conduct and character of control of freedom of conduct of modern teenagers adults are analysed in the article.В статье анализируются составляющие поведенческой автономии и характер контроля взрослыми поведенческой свободы современных подростков
Universal features of dimensional reduction schemes from general covariance breaking
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors