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A. P. Polychronakos

Publications and source records attributed to A. P. Polychronakos.

At least 19 recordsLinked to original sources
arXiv2012

Fuzzy spaces and new random matrix ensembles

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.

hep-th↗
arXiv2004

Perfect Fluid Theory and its Extensions

We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).

hep-ph↗
arXiv2002

Noncommuting Gauge Fields as a Lagrange Fluid

The Lagrange description of an ideal fluid gives rise in a natural way to a gauge potential and a Poisson structure that are classical precursors of analogous noncommuting entities. With this observation we are led to construct gauge-covariant coordinate transformations on a noncommuting space. Also we recognize the Seiberg-Witten map from noncommuting to commuting variables as the quantum correspondent of the Lagrange to Euler map in fluid mechanics.

hep-th↗
arXiv2001

Spectrum of Schroedinger field in a noncommutative magnetic monopole

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged Schroedinger field coupled to a noncommutative U(1) gauge field is identified. It is shown that the Hamiltonian is essentially the angular momentum squared of the particle, but with a nontrivial scaling factor appearing, in agreement with the first-quantized canonical treatment of the problem. Monopole quantization is recovered and identified as the quantization of a commutative Seiberg-Witten mapped monopole field.

hep-th↗
arXiv2001

Testing Non-commutative QED, Constructing Non-commutative MHD

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.

hep-th↗
arXiv2001

Quantum mechanics on the noncommutative plane and sphere

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.

hep-th↗
arXiv2000

Supersymmetric Fluid Mechanics

When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.

hep-th↗
arXiv2000

Clebsch (String) Parameterization of 3-Vectors and Their Actions

We discuss some properties of the intrinsically nonlinear Clebsch decomposition of a vector field into three scalars in d=3. In particular, we note and account for the incompleteness of this parameterization when attempting to use it in variational principles involving Maxwell and Chern-Simons actions. Similarities with string decomposition of metrics and their actions are also pointed out.

physics.flu-dyn↗
arXiv2000

On area and entropy of a black hole

We consider a model of a black hole consisting of a number of elementary components. Examples of such models occur in the Ashtekar's approach to canonical Quantum Gravity and in M-theory. We show that treating the elementary components as completely distinguishable leads to the area law for the black hole entropy. Contrary to previous results, we show that no Bose condensation occurs, the area has big local fluctuations and that in the framework of canonical Quantum Gravity the area of the black hole horizon is equidistantly quantized.

hep-th↗
arXiv1999

Fluid Dynamical Profiles and Constants of Motion from d-Branes

Various fluid mechanical systems enjoy a hidden, higher-dimensional dynamical Poincare symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there are equivalence transformations between different models. These interconnections are discussed in our paper.

hep-th↗
arXiv1998

Dynamical Poincare Symmetry Realized by Field-dependent Diffeomorphisms

We present several Galileo invariant Lagrangians, which are invariant against Poincare transformations defined in one higher (spatial) dimension. Thus these models, which arise in a variety of physical situations, provide a representation for a dynamical (hidden) Poincare symmetry. The action of this symmetry transformation on the dynamical variables is nonlinear, and in one case involves a peculiar field-dependent diffeomorphism. Some of our models are completely integrable, and we exhibit explicit solutions.

hep-th↗
arXiv1997

On The Instanton Solutions Of The Self-Dual Membrane In Various Dimensions

We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to play a central role, and a specific method of determining all the periodic solutions are suggested. A number of examples are studied in detail.

hep-th↗
arXiv1996

Path Integrals and Parastatistics

The propagator and corresponding path integral for a system of identical particles obeying parastatistics are derived. It is found that the statistical weights of topological sectors of the path integral for parafermions and parabosons are simply related through multiplication by the parity of the permutation of the final positions of the particles. Appropriate generalizations of statistics are proposed obeying unitarity and factorizability (strong cluster decomposition). The realization of simple maximal occupancy (Gentile) statistics is shown to require ghost states.

hep-th↗
arXiv1995

Solitons and fractional statistics

Solitons in the continuum limit of the Calogero model are derived and shown to correspond to one-particle excitations. The statistical mechanics of exclusion statistics particles is then formulated in terms of a priori probabilities and a path integral is thereoff constructed. (Talk delivered at the Trieste April 1995 Conference on statistical mechanics and QFT and at the Oslo August 1995 Worskhop on low-dimensional systems.)

cond-mat↗