Finite field equation of Yang–Mills theory

1980 ◽  
Vol 21 (3) ◽  
pp. 547-560
Author(s):  
Richard A. Brandt ◽  
Ng Wing‐Chiu ◽  
Wai‐Bong Yeung
Keyword(s):  
Field Equation ◽  
Finite Field ◽  
Yang Mills

Finite field equation for asymptotically freeφ4theory

1979 ◽  
Vol 19 (2) ◽  
pp. 503-510 ◽  
Author(s):  
Richard A. Brandt ◽  
Ng Wing-chiu ◽  
Yeung Wai-Bong
Keyword(s):  
Field Equation ◽  
Finite Field

scholarly journals CONNECTING GREEN FUNCTIONS IN AN ARBITRARY PAIR OF GAUGES AND AN APPLICATION TO PLANAR GAUGES

2001 ◽  
Vol 16 (31) ◽  
pp. 5043-5059 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Green Function ◽  
Finite Field ◽  
Path Integrals ◽  
Green Functions ◽  
Expectation Values ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Field Dependent ◽  
Gauge Connection ◽  
Arbitrary Gauge

We establish a finite field-dependent BRS transformation that connects the Yang–Mills path integrals with the Faddeev–Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green function (either a primary one or that of an operator) in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge Fby its construction. This is because the construction preserves expectation values of gauge-invariant observables. We establish parallel results also for the planar gauge-Lorentz gauge connection.

scholarly journals CONSERVED CURRENT FOR GENERAL TELEPARALLEL MODELS

2002 ◽  
Vol 17 (20) ◽  
pp. 2765-2765 ◽  
Author(s):  
Y. ITIN
Keyword(s):  
Field Equation ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Geometrical Structures ◽  
Yang Mills ◽  
First Order ◽  
Diffeomorphism Invariance ◽  
Maxwell Field Equation ◽  
Conserved Current

The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures1,2. A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑa is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity) 3. By introducing the notion of a 3-parameter conjugate field strength F linear in the strength Ca = dϑa the coframe Lagrangian is rewritten in the Maxwell-Yang-Mills form L = 1/2Fa ∧ Ca. The field equation turns out to have a form d * Fa = Ta completely similar to the Maxwell field equation. By applying the Noether procedure, the source 3-form Ta is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source Ta of the coframe field is interpreted as the total conserved energy-momentum current of the coframe field and matter4. The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields 5. Thus an energy-momentum tensor for the coframe is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in the standard GR. The result is: The standard GR has a neighborhood of viable models with the same Schwarzschild solutions. These models however have a better Lagrangian behavior and produce an invariant energy-momentum tensor.

scholarly journals Fractional derivative of inverse matrix and its applications to soliton theory

2020 ◽  
Vol 24 (4) ◽  
pp. 2597-2604
Author(s):  
Sheng Zhang ◽  
Jiao Gao ◽  
Bo Xu
Keyword(s):  
Field Equation ◽  
Fractional Derivative ◽  
Partial Derivative ◽  
Inverse Matrix ◽  
Chiral Field ◽  
Soliton Theory ◽  
Yang Mills ◽  
Principal Chiral Field ◽  
Linear Pde ◽  
Non Linear

In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.

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