18,527 research outputs found
Position-dependent noncommutativity in quantum mechanics
The model of the position-dependent noncommutativety in quantum mechanics is
proposed. We start with a given commutation relations between the operators of
coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of
commutation relations, including the operators of momenta. The constructed
algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi
identity. The key point of our construction is a proposed first-order
Lagrangian, which after quantization reproduces the desired commutation
relations. Also we study the possibility to localize the noncommutativety.Comment: published version, references adde
Equivalence classes for gauge theories
In this paper we go deep into the connection between duality and fields
redefinition for general bilinear models involving the 1-form gauge field .
A duality operator is fixed based on "gauge embedding" procedure. Dual models
are shown to fit in equivalence classes of models with same fields
redefinitions
Noncommutativity due to spin
Using the Berezin-Marinov pseudoclassical formulation of spin particle we
propose a classical model of spin noncommutativity. In the nonrelativistic
case, the Poisson brackets between the coordinates are proportional to the spin
angular momentum. The quantization of the model leads to the noncommutativity
with mixed spacial and spin degrees of freedom. A modified Pauli equation,
describing a spin half particle in an external e.m. field is obtained. We show
that nonlocality caused by the spin noncommutativity depends on the spin of the
particle; for spin zero, nonlocality does not appear, for spin half, , etc. In the relativistic case the noncommutative
Dirac equation was derived. For that we introduce a new star product. The
advantage of our model is that in spite of the presence of noncommutativity and
nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation
it gives noncommutativity with a nilpotent parameter.Comment: 11 pages, references adda
Duality and fields redefinition in three dimensions
We analyze local fields redefinition and duality for gauge field theories in
three dimensions. We find that both Maxwell-Chern-Simons and the Self-Dual
models admits the same fields redefinition. Maxwell-Proca action and its dual
also share this property. We show explicitly that a gauge-fixing term has no
influence on duality and fields redefinition.Comment: 8 pages, suppressed contents. To appear in J. Phys.
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