2,058 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 $\theta^{-1}$. By "internal" we mean
that the effective magnetic fields depends essentially on the particle
properties and modifies the symplectic structure. Here $\theta$ 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
$\beta$ - 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 $\beta$ 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

### 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

### 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

### 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.

### A New Interpretation of the Seiberg Witten Map

In an alternative interpretation, the Seiberg-Witten map is shown to be
induced by a field dependent co-ordinate transformation connecting
noncommutative and ordinary space-times. Furthermore, following our previous
ideas, it has been demonstrated here that the above (field dependent
co-ordinate) transformation can occur naturally in the Batalin-Tyutin extended
space version of the relativistic spinning particle model, (in a particular
gauge). There is no need to postulate the space-time non-commutativity in an
{\it ad hoc} way: It emerges from the spin degrees of freedom.Comment: Minor changes in the text, version to appear in J.Phys. A (Letter
Section

### Space-Time Symmetries in Noncommutative Gauge Theory: A Hamiltonian Analysis

We study space-time symmetries in Non-Commutative (NC) gauge theory in the
(constrained) Hamiltonian framework. The specific example of NC CP(1) model,
posited in \cite{sg}, has been considered. Subtle features of Lorentz
invariance violation in NC field theory were pointed out in \cite{har}. Out of
the two - Observer and Particle - distinct types of Lorentz transformations,
symmetry under the former, (due to the translation invariance), is reflected in
the conservation of energy and momentum in NC theory. The constant tensor
$\theta_{\mu\nu}$ (the noncommutativity parameter) destroys invariance under
the latter.
In this paper we have constructed the Hamiltonian and momentum operators
which are the generators of time and space translations respectively. This is
related to the Observer Lorentz invariance. We have also shown that the
Schwinger condition and subsequently the Poincare algebra is not obeyed and
that one can not derive a Lorentz covariant dynamical field equation. These
features signal a loss of the Particle Lorentz symmetry. The basic observations
in the present work will be relevant in the Hamiltonian study of a generic
noncommutative field theory.Comment: 12 pages, Latex, modified version, no change in maths. part, 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

- …