68 research outputs found
Twistor formulation of a massive particle with rigidity
A massive rigid particle model in dimensions is reformulated in terms
of twistors. Beginning with a first-order Lagrangian, we establish a twistor
representation of the Lagrangian for a massive particle with rigidity. The
twistorial Lagrangian derived in this way remains invariant under a local transformation of the twistor and other relevant variables.
Considering this fact, we carry out a partial gauge-fixing so as to make our
analysis simple and clear. We develop the canonical Hamiltonian formalism based
on the gauge-fixed Lagrangian and perform the canonical quantization procedure
of the Hamiltonian system. Also, we obtain an arbitrary-rank massive spinor
field in dimensions via the Penrose transform of a twistor function
defined in the quantization procedure. Then we prove, in a twistorial fashion,
that the spin quantum number of a massive particle with rigidity can take only
non-negative integer values, which result is in agreement with the one shown
earlier by Plyushchay. Interestingly, the mass of the spinor field is
determined depending on the spin quantum number.Comment: 50 pages, Section 6 is revised, A reference added, minor corrections,
Published versio
Abelian Projection of Massive SU(2) Yang-Mills Theory
We derive an effective Abelian gauge theory (EAGT) of a modified SU(2)
Yang-Mills theory. The modification is made by explicitly introducing mass
terms of the off-diagonal gluon fields into pure SU(2) Yang-Mills theory, in
order that Abelian dominance at a long-distance scale is realized in the
modified theory. In deriving the EAGT, the off-diagonal gluon fields involving
longitudinal modes are treated as fields that produce quantum effects on the
diagonal gluon field and other fields relevant at a long-distance scale. Unlike
earlier papers, a necessary gauge fixing is carried out without spoiling the
global SU(2) gauge symmetry. We show that the EAGT allows a composite of the
Yukawa and the linear potentials which also occurs in an extended dual Abelian
Higgs model. This composite potential is understood to be a static potential
between color-electric charges. In addition, we point out that the EAGT
involves the Skyrme-Faddeev model.Comment: 24 pages, title changed, minor changes, references added, to appear
in Mod. Phys. Lett.
Second quantized formulation of geometric phases
The level crossing problem and associated geometric terms are neatly
formulated by the second quantized formulation. This formulation exhibits a
hidden local gauge symmetry related to the arbitrariness of the phase choice of
the complete orthonormal basis set. By using this second quantized formulation,
which does not assume adiabatic approximation, a convenient exact formula for
the geometric terms including off-diagonal geometric terms is derived. The
analysis of geometric phases is then reduced to a simple diagonalization of the
Hamiltonian, and it is analyzed both in the operator and path integral
formulations. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial (and thus
no monopole singularity) for arbitrarily large but finite time interval .
The integrability of Schr\"{o}dinger equation and the appearance of the
seemingly non-integrable phases are thus consistent. The topological proof of
the Longuet-Higgins' phase-change rule, for example, fails in the practical
Born-Oppenheimer approximation where a large but finite ratio of two time
scales is involved and is identified with the period of the slower system.
The difference and similarity between the geometric phases associated with
level crossing and the exact topological object such as the Aharonov-Bohm phase
become clear in the present formulation. A crucial difference between the
quantum anomaly and the geometric phases is also noted.Comment: 22 pages, 3 figures. The analysis in the manuscript has been made
more precise by including a brief account of the hidden local gauge symmetry
and by adding several new equations. This revised version is to be published
in Phys. Rev.
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