scholarly journals BOSONIZATION OF NON-RELATIVISTIC FERMIONS AND W-INFINITY ALGEBRA

1992 ◽  
Vol 07 (01) ◽  
pp. 71-83 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA
Keyword(s):  
Magnetic Field ◽  
External Field ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Cartan Subalgebra ◽  
Space Dimension ◽  
Three Dimensional ◽  
Classical Action ◽  
Yang Mills ◽  
The One

We discuss the bosonization of non-relativistic fermions in one-space dimension in terms of bilocal operators which are naturally related to the generators of W-infinity algebra. The resulting system is analogous to the problem of a spin in a magnetic field for the group W-infinity. The new dynamical variables turn out to be W-infinity group elements valued in the coset W-infinity/H where H is a Cartan subalgebra. A classical action with an H gauge invariance is presented. This action is three-dimensional. It turns out to be similar to the action that describes the color degrees of freedom of a Yang–Mills particle in a fixed external field. We also discuss the relation of this action with the one recently arrived at in the Euclidean continuation of the theory using different coordinates.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

MAGNETIC FIELDS AND VACUUM POLARIZATION AT THE PLANCK ERA

2003 ◽  
Vol 12 (07) ◽  
pp. 1289-1298 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vacuum State ◽  
Background Field ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Maxwell Theory ◽  
Yang Mills ◽  
Electron Positron ◽  
The One

The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

ON GAUGE INVARIANCE OF THE COVARIANT ACTION OF THE GREEN-SCHWARZ SUPERSTRING

1989 ◽  
Vol 04 (17) ◽  
pp. 1685-1689
Author(s):  
T. HORI ◽  
K. KAMIMURA
Keyword(s):  
Gauge Invariance ◽  
Chiral Model ◽  
World Sheet ◽  
Classical Action ◽  
Model Type ◽  
Lorentzian Metric ◽  
Covariant Action ◽  
The One

The gauge invariance of the covariant classical action of the Green-Schwarz superstring with Euclidean world sheet metric is examined. The action in terms of the Majorana-Weyl spinors is shown to exist only for the chiral model (type IIB). This action coincides with the one analytically continued from the Lorentzian metric when the Majorana condition is suitably modifed.

A First Example: The “Particle in a Box“ and Quantized Translational Motion

2020 ◽  
pp. 59-96
Author(s):  
Jochen Autschbach
Keyword(s):  
Degrees Of Freedom ◽  
Separation Of Variables ◽  
Translational Motion ◽  
Three Dimensional ◽  
Potential Wells ◽  
Quantum Tunnelling ◽  
Atomic Force ◽  
Quantum Behavior ◽  
The One ◽  
Three Degrees Of Freedom

The simple ‘particle in a box’ (Piab) is introduced in this chapter so that the reader can get familiar with applying the quantum recipe and atomic units. The PiaB is introduced in its one, two, and three dimensional variants, which demonstrates the use of the separation of variables technique as a strategy to solve the Schrodinger equation for a particle with two or three degrees of freedom. It is shown that the confinement of the particle causes the energy to be quantized. The one-dimensional PiaB is then applied to treat the electronic spectra of cyanine dyes and their absorption colors. The chapter then introduces more general setups with finite potential wells, in order to introduce the phenomenon of quantum tunnelling and to discuss more generally with the unintuitive ‘quantum behavior’ of particles such as electrons. Scanning tunnelling and atomic force microscopes are also discussed briefly.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

1992 ◽  
Vol 07 (02) ◽  
pp. 235-256 ◽  
Author(s):  
MANUEL ASOREY ◽  
FERNANDO FALCETO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Condition ◽  
Simons Theory ◽  
Coupling Constant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
The One ◽  
Chern Simons ◽  
Three Dimensional Space

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

scholarly journals Ears on the Hand: Reaching Three-Dimensional Targets With an Audio-Motor Device

2020 ◽  
Vol 33 (4-5) ◽  
pp. 433-455 ◽  
Author(s):  
Sylvain Hanneton ◽  
Thomas Hoellinger ◽  
Vincent Forma ◽  
Agnes Roby-Brami ◽  
Malika Auvray
Keyword(s):  
Degrees Of Freedom ◽  
Body Movement ◽  
Three Dimensional ◽  
Sensory Substitution ◽  
Dominant Hand ◽  
Coupling Condition ◽  
Electromagnetic System ◽  
3D Audio ◽  
Auditory Experience ◽  
The One

Abstract Understanding the processes underlying sensorimotor coupling with the environment is crucial for sensorimotor rehabilitation and sensory substitution. In doing so, devices which provide novel sensory feedback consequent to body movement may be optimized in order to enhance motor performance for particular tasks. The aim of the study reported here was to investigate audio-motor coupling when the auditory experience is linked to movements of the head or the hands. The participants had to localize and reach a virtual source with the dominant hand in response to sounds. An electromagnetic system recorded the position and orientation of the participants’ head and hands. This system was connected to a 3D audio system that provided binaural auditory feedback on the position of the virtual listener located on the participants’ body. The listener’s position was computed either from the hands or from the head. For the hand condition, the virtual listener was placed on the dominant hand (the one used to reach the target) in Experiment 1 and on the non-dominant hand, which was constrained in order to have similar amplitude and degrees of freedom as that of the head, in Experiment 2. The results revealed that, in the two experiments, the participants were able to localize a source within the 3D auditory environment. Performance varied as a function of the effector’s degrees of freedom and the spatial coincidence between sensor and effector. The results also allowed characterizing the kinematics of the hand and head and how they change with audio-motor coupling condition and practice.

scholarly journals Generalized spinning particles on $${\mathcal {S}}^2$$ in accord with the Bianchi classification

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Anton Galajinsky
Keyword(s):  
External Field ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Degrees Of Freedom ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Dirac Monopole ◽  
Spinning Particles ◽  
Group Manifold ◽  
Internal Degrees Of Freedom

AbstractMotivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on $${\mathcal {S}}^2$$ S 2 , the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar models, which rely upon real Lie algebras with dimensions $$d=4,5,6$$ d = 4 , 5 , 6 , is elucidated.

scholarly journals Correlation functions of three-dimensional Yang-Mills theory from the FRG

2018 ◽  
Vol 5 (6) ◽  
Author(s):  
Lukas Corell ◽  
Anton K. Cyrol ◽  
Mario Mitter ◽  
Jan M. Pawlowski ◽  
Nils Strodthoff
Keyword(s):  
Correlation Functions ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Renormalisation Group ◽  
Special Technique ◽  
Classical Action ◽  
Yang Mills ◽  
Truncation Scheme ◽  
Physical Case

We compute correlation functions of three-dimensional Landau-gauge Yang-Mills theory with the Functional Renormalisation Group. Starting from the classical action as only input, we calculate the non-perturbative ghost and gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon, and four-gluon vertices in a comprehensive truncation scheme. Compared to the physical case of four spacetime dimensions, we need more sophisticated truncations due to significant contributions from non-classical tensor structures. In particular, we apply a special technique to compute the tadpole diagrams of the propagator equations, which captures also all perturbative two-loop effects, and compare our correlators with lattice and Dyson-Schwinger results.

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