OBSERVATIONS ON A U(1) × U(1) VECTOR THEORY

2002 ◽  
Vol 17 (16) ◽  
pp. 2211-2217
Author(s):  
D. G. C. MCKEON
Keyword(s):  
Vector Fields ◽  
Equations Of Motion ◽  
Quantization Condition ◽  
Constraint Condition ◽  
Supersymmetric Version ◽  
Dirac Quantization ◽  
Covariant Gauge ◽  
Vector Theory ◽  
Two Sectors ◽  
Conserved Currents

The symmetry between two sectors of a model containing two U(1) vector fields (related by a constraint condition) and two conserved currents is examined. The equations of motion for the vector fields, once the constraint condition is applied, is similar in form to the Maxwell equations in the presence of both electric and magnetic charge. The Dirac quantization condition need not be applied. The propagators for the vector fields are computed in a covariant gauge, demonstrating that the model is unitary and renormalizable. A supersymmetric version of the model is presented.

scholarly journals DUALITY IN EQUATIONS OF MOTION FROM SPACE–TIME DEPENDENT LAGRANGIANS

2000 ◽  
Vol 15 (14) ◽  
pp. 901-911 ◽  
Author(s):  
RAJSEKHAR BHATTACHARYYA ◽  
DEBASHIS GANGOPADHYAY
Keyword(s):  
Equations Of Motion ◽  
Space Time ◽  
Quantization Condition ◽  
Time Dependent ◽  
Classical Solutions ◽  
String Solution ◽  
Yang Mills ◽  
Dirac Quantization ◽  
Lagrangian Field Theory ◽  
Condition C

Starting from Lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit space–time dependence of the Lagrangian. Poincaré invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both Abelian and non-Abelian dualities. We illustrate how (a) Dirac string solution, (b) Dirac quantization condition, (c) 't Hooft–Polyakov monopole solutions and (d) a procedure emerges for obtaining new classical solutions of Yang–Mills (YM) theory. Moreover, these results occur in a way that is strongly reminiscent of the holographic principle.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

scholarly journals Ions, Protons, and Photons as Signatures of Monopoles

Universe ◽  
2018 ◽  
Vol 4 (11) ◽  
pp. 117 ◽  
Author(s):  
Vicente Vento
Keyword(s):  
Magnetic Charge ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Two Photon ◽  
Charge Quantization ◽  
Dirac Quantization ◽  
The Relationship ◽  
Charged Ions

Magnetic monopoles have been a subject of interest since Dirac established the relationship between the existence of monopoles and charge quantization. The Dirac quantization condition bestows the monopole with a huge magnetic charge. The aim of this study was to determine whether this huge magnetic charge allows monopoles to be detected by the scattering of charged ions and protons on matter where they might be bound. We also analyze if this charge favors monopolium (monopole–antimonopole) annihilation into many photons over two photon decays.

scholarly journals SUPERSYMMETRIC WZW σ MODEL ON INFINITE AND HALF-PLANE

2005 ◽  
Vol 20 (13) ◽  
pp. 2763-2772
Author(s):  
R. A. ZAIT ◽  
M. F. MOURAD
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Half Plane ◽  
Infinite Number ◽  
Equations Of Motion ◽  
Free Boundary Condition ◽  
Infinite Plane ◽  
Recursion Relations ◽  
Conserved Currents

We study classical integrability of the supersymmetric U(N) σ model with the Wess–Zumino–Witten term on infinite and half-plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit forms of the first few supersymmetric charges are constructed. We show that the considered model is integrable on infinite plane as a consequence of the conservation of the supersymmetric charges. Also, we study the model on half-plane with free boundary, and examine the conservation of the supersymmetric charges on half-plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half-plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.

scholarly journals ISRAEL–WILSON–PERJÉS SOLUTIONS IN HETEROTIC STRING THEORY

1999 ◽  
Vol 14 (09) ◽  
pp. 1345-1356 ◽  
Author(s):  
ALFREDO HERRERA-AGUILAR ◽  
OLEG KECHKIN
Keyword(s):  
String Theory ◽  
Vector Fields ◽  
Equations Of Motion ◽  
Simple Algorithm ◽  
Heterotic String ◽  
Three Dimensions ◽  
Heterotic String Theory ◽  
The Matrix ◽  
Em Theory ◽  
Bosonic Part

We present a simple algorithm to obtain solutions that generalize the Israel–Wilson–Perjés class for the low energy limit of heterotic string theory toroidally compactified from D=d+3 to three dimensions. A remarkable map existing between the Einstein–Maxwell (EM) theory and the theory under consideration allows us to solve directly the equations of motion making use of the matrix Ernst potentials connected with the coset matrix of heterotic string theory.1 For the particular case d=1 (if we put n=6, the resulting theory can be considered as the bosonic part of the action of D=4, N=4 supergravity) we obtain explicitly a dyonic solution in terms of one real 2×2-matrix harmonic function and 2n real constants (n being the number of Abelian vector fields). By studying the asymptotic behavior of the field configurations we define the charges of the system. They satisfy the Bogomol'nyi–Prasad–Sommerfield (BPS) bound.

BOUNDARY CONDITIONS IN THE MECHANICS OF FIELDS

1952 ◽  
Vol 30 (6) ◽  
pp. 684-698
Author(s):  
S. M. Neamtan ◽  
E. Vogt
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Vector Fields ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Second Order ◽  
Dirac Field ◽  
Energy Tensor ◽  
Complex Scalar ◽  
Set Up

A variational principle has been set up for the description of relativistic fields with the aid of Lagrangians involving second order derivatives of the field functions. This constitutes a generalization of the usual formulation in that, besides the boundary conditions usually imposed, it admits also linear homogeneous boundary conditions. The formulation has been developed for the complex scalar and complex vector fields. The variational principle then yields not only the wave equations but also the allowed boundary conditions. A Hamiltonian and equations of motion in canonical form can be set up. A symmetric stress–energy tensor and a charge–current vector are defined, yielding the usual conservation equations. For the vector field, π4 is not identically zero; also the Lorentz condition arises out of the variational principle and does not have to be separately imposed. For the Dirac field an extension to Lagrangians with second order derivatives is not possible, but for this field also the variational principle yields the allowed boundary conditions.

scholarly journals Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds

2018 ◽  
Vol 30 (05) ◽  
pp. 1850012 ◽  
Author(s):  
C. I. Lazaroiu ◽  
C. S. Shahbazi
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Global Solutions ◽  
Mathematical Object ◽  
Mathematical Structure ◽  
Quantization Condition ◽  
Local Analysis ◽  
Abelian Gauge ◽  
Abelian Gauge Theory

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle [Formula: see text] defined over the scalar manifold [Formula: see text]. The construction uses a taming of [Formula: see text], which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of [Formula: see text] to the bundle [Formula: see text] and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over [Formula: see text] and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from [Formula: see text] supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

THE QUANTIZATION OF CLASSICAL SPIN THEORY

1953 ◽  
Vol 31 (1) ◽  
pp. 1-10 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Hamiltonian Dynamics ◽  
Equations Of Motion ◽  
Supplementary Condition ◽  
Poisson Brackets ◽  
Rest System ◽  
Spin Tensor ◽  
Constraint Condition ◽  
Set Up ◽  
Jacobi Equations ◽  
Quantum Formulation

The antisymmetric spin tensor of rank two used to describe the rotational motion of a particle is assumed to satisfy the constraint condition that the velocity 4-vector is orthogonal to it. Since the dipole moment is proportional to the spin tensor, this condition leads always to a purely magnetic dipole in the rest system of the particle. Frenkel has indicated how the action principle for the classical equations of motion can be set up treating the above constraint condition as a supplementary condition. The Hamiltonian dynamics of a system having supplementary conditions and Lagrange undetermined multipliers has been discussed recently by Dirac. Dirac's method and results previously obtained give the required Hamilton–Jacobi equations and Poisson Brackets of the dynamical variables. The cases where the particle behaves like a pure gyroscope and a symmetrical top are treated. When there is an interacting field, it is assumed that the action of the Held is given by the effective 4-vector potential without further specification. The orthogonality of the velocity to the tensor dual to the spin tensor can be imposed as an alternative constraint condition. This possibility is discussed briefly. The quantum formulation is completed with the help of the standard analogy rules.

scholarly journals Dirac quantization condition for monopole in noncommutative space-time

2009 ◽  
Vol 79 (12) ◽  
Author(s):  
Masud Chaichian ◽  
Subir Ghosh ◽  
Miklos Långvik ◽  
Anca Tureanu
Keyword(s):  
Space Time ◽  
Quantization Condition ◽  
Noncommutative Space ◽  
Dirac Quantization

scholarly journals Visible and hidden sectors in a model with Maxwell and Chern–Simons gauge dynamics

2016 ◽  
Vol 31 (34) ◽  
pp. 1650178 ◽  
Author(s):  
Edwin Ireson ◽  
Fidel A. Schaposnik ◽  
Gianni Tallarita
Keyword(s):  
Gauge Fields ◽  
Field Equations ◽  
Supersymmetric Extension ◽  
Abelian Gauge ◽  
Supersymmetric Version ◽  
Vortex Solutions ◽  
Set Up ◽  
Higgs Portal ◽  
Chern Simons ◽  
Two Sectors

We study a [Formula: see text] gauge theory discussing its vortex solutions and supersymmetric extension. In our set-up, the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern–Simons term. The two sectors interact via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.

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