8,988 research outputs found
On the Nonrelativistic Limit of the phi^4 Theory in 2+1 Dimensions
We study the nonrelativistic limit of the quantum theory of a real scalar
field with quartic self-interaction. The two body scattering amplitude is
written in such way as to separate the contributions of high and low energy
intermediary states. From this result and the two loop computation of the self
energy correction, we determine an effective nonrelativistic action.Comment: 15 pages, 2 figures, revte
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
Dynamical Lorentz and CPT symmetry breaking in a 4D four-fermion model
In a 4D chiral Thirring model we analyse the possibility that radiative
corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By
studying the effective potential, we verified that the chiral current
may assume a nonzero vacuum expectation
value which triggers the Lorentz and CPT violations. Furthermore, by making
fluctuations on the minimum of the potential we dynamically induce a bumblebee
like model containing a Chern-Simons term.Comment: Small modifications in the text and new references added, 12 pages, 4
figures, revtex4. To appear in Phys. Rev.
The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions
We study the nonrelativistic limit of the theory of a quantum Chern--Simons
field minimally coupled to Dirac fermions. To get the nonrelativistic effective
Lagrangian one has to incorporate vacuum polarization and anomalous magnetic
moment effects. Besides that, an unsuspected quartic fermionic interaction may
also be induced. As a by product, the method we use to calculate loop diagrams,
separating low and high loop momenta contributions, allows to identify how a
quantum nonrelativistic theory nests in a relativistic one.Comment: 18 pages, 8 figures, Late
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