2,296 research outputs found
A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space
In this paper we have studied a new form of Non-Commutative (NC) phase space
with an operatorial form of noncommutativity. A point particle in this space
feels the effect of an interaction with an "{\it{internal}}" magnetic field,
that is singular at a specific position . By "internal" we mean
that the effective magnetic fields depends essentially on the particle
properties and modifies the symplectic structure. Here is the NC
parameter and induces the coupling between the particle and the "internal"
magnetic field. The magnetic moment of the particle is computed. Interaction
with an {\it{external}} physical magnetic field reveals interesting features
induced by the inherent fuzziness of the NC phase space: introduction of
non-trivial structures into the charge and mass of the particle and possibility
of the particle dynamics collapsing to a Hall type of motion. The dynamics is
studied both from Lagrangian and symplectic (Hamiltonian) points of view. The
canonical (Darboux) variables are also identified. We briefly comment, that the
model presented here, can play interesting role in the context of (recently
observed) {\it{real}} space Berry curvature in material systems.Comment: 8 pages LaTex, Matches journal version, PLB 638 (2006)350; One
reference added and minor change in text, related to i
Quantum Gravity Effects in Geodesic Motion and Predictions of Equivalence Principle Violation
We show that the Equivalence Principle (EP) is violated by Quantum Gravity
(QG) effects. The predicted violations are compared to experimental
observations for Gravitational Redshift, Law of Reciprocal Action and
Universality of Free Fall. This allows us to derive explicit bounds for
- the QG scale.
In our approach, there appears a deviation in the geodesic motion of a
particle. This deviation is induced by a non-commutative spacetime, consistent
with a Generalized Uncertainty Principle (GUP). GUP admits the presence of a
minimum length scale, that is advocated by QG theories. Remarkably, the GUP
induced corrections are quite robust since the bound on obtained by us,
{\it{in General Relativity scenario in an essentially classical setting}} of
modified geodesic motion, is closely comparable to similar bounds in recent
literature \cite{vag}. The latter are computed in purely {\it{quantum}} physics
domain in {\it{flat}} spacetime.Comment: Title changed, Universality of Free Fall expt. added, references
added, modified version, to appear in CQ
The Seiberg-Witten Map in Noncommutative Field Theory: An Alternative Interpretation
In this article, an alternative interpretation of the Seiberg-Witten map in
non-commutative field theory is provided. We show that the Seiberg-Witten map
can be induced in a geometric way, by a field dependent co-ordinate
transformation that connects noncommutative and ordinary space-times.
Furthermore, in continuation of our earlier works, it has been demonstrated
here that the above (field dependent co-ordinate) transformations are present
in a gauge fixed version of the relativistic spinning particle model, embedded
in the Batalin-Tyutin extended space. We emphasize that the space-time
non-commutativity emerges naturally from the particle {\it {spin}} degrees of
freedom. Contrary to similarly motivated works, the non-commutativity is not
imposed here in an {\it{ad-hoc}} manner.Comment: To appear in the special issue of the journal "Relativity,
Gravitation, Cosmology
Wavepackets and Duality in Noncommutative Planar Quantum Mechanics
Effects of noncommutativity are investigated in planar quantum mechanics in
the coordinate representation. Generally these issues are addressed by
converting to the momentum space. In the first part of the work we show
noncommutative effects in a Gaussian wavepacket through the broadening of its
width. We also rederive results on *-product of Gaussian wavepackets. In the
second part, we construct a "Master" model for a noncommutative harmonic
oscillator by embedding it in an extended space. Different gauge choices
leading to different forms of noncommutativity, (such as between coordinates
only, between momenta only or noncommutativity of a more general kind), can be
studied in a unified and systematic manner. Thus the dual nature of these
theories are also revealed.Comment: Latex, The first part on wave packets is expanded and rewritten,
Results and conclusions are unchange
Spontaneous Generation of a Crystalline Ground State in a Higher Derivative Theory
The possibility of Spontaneous Symmetry Breaking in momentum space in a
generic Lifshitz scalar model - a non-relativistic scalar field theory with
higher spatial derivative terms - has been studied. We show that the minimum
energy state, the ground state, has a lattice structure, where the translation
invariance of the continuum theory is reduced to a discrete translation
symmetry. The scale of translation symmetry breaking (or induced lattice
spacing) is proportional to the inverse of the momentum of the condensate
particle.
The crystalline ground state is stable under excitations below a certain
critical velocity. The small fluctuations above the ground state can have a
phonon like dispersion under suitable choice of parameters.
At the beginning we have discussed the effects of next to nearest neighbour
interaction terms in a model of linear triatomic molecule depicted by a linear
system of three particles of same mass connected by identical springs. This
model is relevant since in the continuum limit the next to nearest neighbour
interaction terms generate higher (spatial) derivative wave equation, the main
topic of this paper.Comment: Paper revised, title changed, change in interpretation of previous
results, references added, accepted for publication in Physica
Anyons in Electromagnetic Field and the BMT Equation
The Lagrangian model for anyon, presented in [6], is extended to include
interactions with external, homogeneous electromagnetic field. Explicit
electric and magnetic moment terms for the anyon are introduced in the
Lagrangian. The 2+1-dimensional BMT equation as well as the correct value (2)
of the gyromagnetic ratio is rederived, in the Hamiltonian framework.Comment: Latex file, 10 pages, GHC-TH/94-0
Noncommutativity in Maxwell-Chern-Simons-Matter Theory Simulates Pauli Magnetic Coupling
We study interactions between like charges in the noncommutative
Maxwell-Chern-Simons electrodynamics {\it{minimally}} coupled to spinors or
scalars. We demonstrate that the non-relativistic potential profiles, for only
spatial noncommutativity, are nearly identical to the ones generated by a
{\it{non-minimal}} Pauli magnetic coupling, originally introduced by Stern
\cite{js}. Although the Pauli term has crucial roles in the context of
physically relevant objects such as anyons and like-charge bound states (or
"Cooper pairs"), its inception \cite{js} (see also \cite{others}) was ad-hoc
and phenomenological in nature. On the other hand we recover similar results by
extending the minimal model to the noncommutative plane, which has developed in
to an important generalization to ordinary spacetime in recent years. No
additional input is needed besides the noncommutativity parameter.
We prove a novel result that for complex scalar matter sector, the bound
states (or "Cooper pairs" can be generated {\it{only}} if the
Maxwell-Chern-Simons-scalar theory is embedded in noncommutative spacetime.
This is all the more interesting since the Chern-Simons term does not directly
contribute a noncommutative correction term in the action.Comment: Revised version, Title changed, No changes in maths. part and
conclusions, To appear in Mod.Phys.Lett.
Poincare Anomaly in Planar Field Theory
We show the presence of Poincare anomaly in Maxwell-Chern-Simons theory with
an explicit mass term, in 2+1-dimensions.Comment: 7 pages, Late
Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly
In this Letter we have derived the gravitational anomaly leading to the
Hawking radiation from a fundamentally different perspective: it emerges due to
the {\it{complimentary}} roles played by tunneling and (gravitational) anomaly.
We have used the analogy of an early idea \cite{niel1} of visualizing chiral
gauge anomaly as an effect of {\it{spectral flow}} of the energy levels, from
the negative energy Dirac sea, across zero energy level in presence of gauge
interactions. This was extended to conformal anomaly in \cite{fumita}. In the
present work, we exploit the latter formalism in black hole physics where we
interpret crossing the horizon of black hole (the zero energy level) as a
spectral flow since it is also accompanied by a change of sign in the energy of
the particle. Hence in our formulation the negative energy states below horizon
play a similar role as the Dirac sea. We successfully recover the gravitational
anomaly.Comment: Title and abstract changed, paper thoroughly rewritten, no change in
basic idea and framework, to appear in Mod.Phys.Lett.
Anyon Zitterbewegung
A new model for anyon is proposed, which exhibits the classical analogue of
the quantum phenomenon - Zitterbewegung. The model is derived from existing
spinning particle model and retains the essential features of anyon in the
non-relativistic limit.Comment: 5 pages, Latex; email:[email protected]
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