64 research outputs found
A path integral leading to higher-order Lagrangians
We consider a simple modification of standard phase-space path integrals and
show that it leads in configuration space to Lagrangians depending also on
accelerations.Comment: 6 page
Discrete Nonlocal Waves
We study generic waves without rotational symmetry in (2+1) - dimensional
noncommutative scalar field theory. In the representation chosen, the radial
coordinate is naturally rendered discrete. Nonlocality along this coordinate,
induced by noncommutativity, accounts for the angular dependence of the fields.
The exact form of standing and propagating waves on such a discrete space is
found in terms of finite series. A precise correspondence is established
between the degree of nonlocality and the angular momentum of a field
configuration. At small distance no classical singularities appear, even at the
location of the sources. At large radius one recovers the usual commutative
behaviour.Comment: 20 page
Lagrangian versus Quantization
We discuss examples of systems which can be quantized consistently, although
they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde
Field Theory of Tachyon Matter
We propose a field theory for describing the tachyon on a brane-antibrane
system near the minimum of the potential. This field theory realizes two known
properties of the tachyon effective action: 1) absence of plane-wave solutions
around the minimum, and 2) exponential fall off of the pressure at late time as
the tachyon field evolves from any spatially homogeneous initial configuration
towards the minimum of the potential. Classical solutions in this field theory
include non-relativistic matter with arbitrary spatial distribution of energy.Comment: LaTeX file, 9 pages, discussion of classical solutions expanded,
other minor change
The 4th International Conference on Social Responsibility, Ethics, and Sustainable Business. Athens, Greece, October 8 & 9, 2015
Magnetic fields in noncommutative quantum mechanics
We discuss various descriptions of a quantum particle on noncommutative space
in a (possibly non-constant) magnetic field. We have tried to present the basic
facts in a unified and synthetic manner, and to clarify the relationship
between various approaches and results that are scattered in the literature.Comment: Dedicated to the memory of Julius Wess. Work presented by F. Gieres
at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007
Quantum mechanics on non commutative spaces and squeezed states: a functional approach
We review here the quantum mechanics of some noncommutative theories in which
no state saturates simultaneously all the non trivial Heisenberg uncertainty
relations. We show how the difference of structure between the Poisson brackets
and the commutators in these theories generically leads to a harmonic
oscillator whose positions and momenta mean values are not strictly equal to
the ones predicted by classical mechanics.
This raises the question of the nature of quasi classical states in these
models. We propose an extension based on a variational principle. The action
considered is the sum of the absolute values of the expressions associated to
the non trivial Heisenberg uncertainty relations. We first verify that our
proposal works in the usual theory i.e we recover the known Gaussian functions.
Besides them, we find other states which can be expressed as products of
Gaussians with specific hyper geometrics.
We illustrate our construction in two models defined on a four dimensional
phase space: a model endowed with a minimal length uncertainty and the non
commutative plane. Our proposal leads to second order partial differential
equations. We find analytical solutions in specific cases. We briefly discuss
how our proposal may be applied to the fuzzy sphere and analyze its
shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and
misprints have been corrected. Version to appear in JHE
Worldline approach to noncommutative field theory
The study of the heat-trace expansion in noncommutative field theory has
shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are
related to the UV/IR mixing and manifest, in some cases, the
non-renormalizability of the theory. We show that these models can be studied
in a worldline approach implemented in phase space and arrive to a master
formula for the -point contribution to the heat-trace expansion. This
formulation could be useful in understanding some open problems in this area,
as the heat-trace expansion for the noncommutative torus or the introduction of
renormalizing terms in the action, as well as for generalizations to other
nonlocal operators.Comment: 19 pages, version
A note on the decay of noncommutative solitons
We propose an ansatz for the equations of motion of the noncommutative model
of a tachyonic scalar field interacting with a gauge field, which allows one to
find time-dependent solutions describing decaying solitons. These correspond to
the collapse of lower dimensional branes obtained through tachyon condensation
of unstable brane systems in string theory.Comment: 8 pages, no figures. Extended version, references adde
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