scholarly journals ON THE CONSTRAINT ALGEBRA STRUCTURE FOR SYSTEMS WITH GAUGE TRANSFORMATIONS DEPENDING ON HIGHER ORDER TIME DERIVATIVES OF THE GAUGE PARAMETERS

2008 ◽  
Vol 23 (11) ◽  
pp. 815-823
Author(s):  
M. N. STOILOV

In the Hamiltonian approach to the gauge models, the constraints on the one hand and the Hamiltonian and constraints on the other hand have to form closed algebras with respect to the Poisson brackets. We investigate the consequences of this requirement when the dynamical system is invariant under gauge transformations with higher order time derivatives of the gauge parameter. It is demonstrated that the required algebraic structure leads to rigid relations in the constraint algebra.

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.


1996 ◽  
Vol 11 (29) ◽  
pp. 5279-5302 ◽  
Author(s):  
KH. S. NIROV

For a wide class of mechanical systems, invariant under gauge transformations with arbitrary higher order time derivatives of gauge parameters, the equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is shown that the Ostrogradsky formalism establishes the natural rules to relate the BFV ghost canonical pairs with the ghosts and antighosts introduced by the Lagrangian approach. Explicit relation between corresponding gauge-fixing terms is obtained.


2021 ◽  
Vol 81 (5) ◽  
Author(s):  
M. Costa ◽  
H. Herodotou ◽  
P. Philippides ◽  
H. Panagopoulos

AbstractWe study the mixing of the Gluino-Glue operator in $$\mathcal{N}=1$$ N = 1 Supersymmetric Yang–Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not merely multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green’s functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $${\overline{\mathrm{MS}}}$$ MS ¯ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson’s formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $$N_c$$ N c , the gauge parameter, $$\beta $$ β , and the clover coefficient, $$c_{\mathrm{SW}}$$ c SW , are left as free parameters.


Author(s):  
Peter Mann

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.


Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.


Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Ion Vancea

AbstractWe generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.


2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.


1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.


PEDIATRICS ◽  
1962 ◽  
Vol 29 (5) ◽  
pp. 714-728
Author(s):  
H. Ghadimi ◽  
M. W. Partington ◽  
A. Hunter

A 3-year-old girl with fair hair and blue eyes came under observation because of speech retardation. The patient was given a phenylalanine-free diet, since persistently positive urine tests with ferric chloride and reagent strips (Phenistix) were strongly suggestive of phenylketonuria. On further investigation she was found to be suffering from a totally different and not heretofore recognized condition, the salient features of which were an abnormally high concentration of histidine in the blood and an excessive output of histidine in the urine. The child's sister, one year older, presented the same metabolic anomaly. In each case both the concentration of histidine in plasma and the daily output were directly related to the amount of protein in the diet; but even at their lowest levels they greatly exceeded those of normal children of the same age. An oral load of histidine was followed by an increase of histidine in plasma much higher and more prolonged than that observed in controls, and by the excretion of a much larger fraction of the ingested dose. The urine of each sister contained not only excessive amounts of histidine but also notable quantities of imidazole-pyruvic, imidazole-acetic, and imidazole-lactic acid, histidine derivatives of which normal urine contains only traces. It is concluded that in the two sisters the normally predominant pathway of histidine catabolism, which leads through urocanic acid to glutamic acid, was partially or completely blocked. Since, even after histidine loading, the urines never contained detectable amounts of urocanic acid, the block must precede the formation of that substance. The condition presented is therefore due primarily to a deficiency or total lack of histidine-alpha-deaminase; the enzyme which converts histidine to urocanic acid. As a result of this defect histidine is forced to take the alternative but less efficient pathway which begins with its transamination to imidazole-pyruvic acid. This substance is the one responsible for positive reactions in the ferric chloride and Phenistix tests. All urine specimens examined, whether from the patient or from normal controls, contained considerable quantities of an unidentifiable imidazole compound ("X"), which does not appear to have been previously reported. The existence of this substance may call for some modification of current concepts of histidine metabolism in man.


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